We teach maths as well as hard work. I teach. We don't cry rage. We work hard I do it my brother. and whoever works hard In teaching or studying, God bless him. He will receive blessings and will progress. To you You will get a job and your children will join us. How many children are studying with a teacher? Yes, how live it is. This is the problem itself No. This is not a discussion at all. Discussion This How many selections after studying from where? There are. That's it. and selections I don't need to tell you. I straight I can say with confidence that the selected The number of photos, shs, reels with children, I included his interview and discussion points. You don't see even 10% anywhere else. will get. Best with selected children Big photo With us. The eldest of the selected children We organize the selection ceremony. My brother. It gives us energy, my Brother. We are energy centers. Got it? name is No Gagan Pratap. Pratap brings energy. young Man is full of energy. That Use your energy wisely in your studies And my brother in teaching. Yes sir? How are you You? Today the second chapter of the number system and this chapter It's the last class and I know half of it The child who was in the first class is dead. Already happened. This is the law of the nature beginning Many people do it. very little until the end Let's reach. That's why 95% of people out of 100 Only 5% of people are below the poverty line. I can reach the upper middle class Brother. So the one who starts is a big deal. Not there. who reaches the end who reaches the last Who will stay, each class will do every one He will read it for a minute and solve every question. Selection will take place because my real aim And there is no emotion between you. This is live Strong, this is not boasting. The real thing, dear friends, which is important The thing is that it is only and only your selection. That's it. If your selection is for something other than your job Anywhere something happens on YouTube, someone If the teacher or anyone else does it, it is your matter. It is totally useless nonsense and junk. Is it okay my brother? You should only care about one thing. The teacher teaches well. Have useful content, Stuck in paper. I took the paper from his studies I will come back after correcting the question. Get a good score, I should get a job and get married. To the teacher I Should I deliver sweets? That's it. think the game is over Children, yes, don't make this comment today. We will completely clear the mess of the number system. How are you feeling dear brothers? The child is saying, Sir, tell me in English also. Brother, I know as much English as I can. I will tell him that much now. I need to learn English to explain more. You will have to, my brother, first of all, you all are from India. Thank you very much dear children That our 30 days of this entire batch The first maths class is number system 24 More than 20 lakh in less than an hour The children have seen that class. Although Our audience is mostly She only watches the recorded class. But his Despite this, children also came and studied live. I also watched a lot of recorded videos. So I enjoyed it Brother. This is how you create love support Keep it. I promise that good I will teach. I will teach you what is useful to you and whatever I will teach you what you will see in the exam. Work Will come. Is it okay my brother? Come on sir. So today I guarantee the class number system Am. You write it down. A question for sure It will come in the paper. In prelims as well as in mains Too. A class for sure. One question for sure. So We will end the number system today. the next class In that we will read LCM and HCF My brother. Next chapter LCM and HCF. After that we will start arithmetic. ok sir. Look, my brother, some time ago we visited a lot of children who Those who were struggling to prepare for government jobs Was in the process of doing it. who are working hard Were. What is success, right? which one you Want to bring transition into your life? To you We have to bring our transition from here to here. These are the kids who are working hard. Many of these children also waste time. Have been. And some of these children Only those who work hard in the right direction. I read it daily and remain consistent. They Are selected. Dear children. Any Someone becomes an Income Tax Inspector Becomes a GST Inspector. Girls too She is achieving a good position. So from here Reaching here is just around the corner for the next six months. The only goal of your life in months Should be. That's it. Do you understand my Brother? And I will get it done, my love From you friends. ok sir. all the children Our Application Selection with Test Download the ranking that I am giving you here. I am teaching concepts, I am teaching theory. Yes, I am getting you practicing, example I am getting it done. Apart from that you can also read previous year Questions of whatever chapter I am teaching I am here, you can attempt it for free. It's okay if you don't have any books. Any You don't need a PDF for this. On application you will get sectional full length Chapter wise full tests will be available for free Children. The only application in India that Most of the mock tests are free. And Dear friends, this is our first class. There was his PDF of number system etc. We have now uploaded the class PAG on our Telegram channel. Whatever is there, I have uploaded it. You can download and see You can. We will upload that as well. Friend. This can last as long as the 30 days batch lasts. It's going to be a complete playlist. Have given. Look, I can say that YouTube's most popular math playlist This will be it. This will be the case with every other child. It will be recommended after 2026 result. This is my promise. ok dear Children? So I have made this entire playlist. All the classes that will be there in future will be added to this. It will keep happening. Okay, right? Share far and wide Do it my friends. It should be fun. Are? And all the children who are studying Like it again and tell me what's happening tomorrow How was the class? Which child has seen the entire class? Tell me how did you like yesterday's class? I am sad. Why brother? Which stone fell on you? Is it true that you are sad? Ok? Let's get started Let's do it today my dear friends Class. It will be a lot of fun. Look at us one You achieved success in a day, not in a day. The desired job will come into your hands. many years It has taken us a long time to work but you have had years to Don't rub it. You only have a few months Have to rub. If you work for 10 hours daily Eliminate distractions and focus on yourself. If you study for 810 months, this cannot happen. My brother, that you may not get the desired result. But for that you will have to go to all the places in the world Pay attention to things that happen on social media You have to remove it and concentrate on yourself. You your Invest your energy in something else. So how will you achieve anything in life? Correct Is? So success is not achieved in a day. One day you will definitely get success if you work hard. I have seen it dear friend. ok sir? So let's start, dear brother. Number System number system class to 0 to hero. Yes brother, our Babu Bhaiya has also come. Hey brother, enjoy Raju and Shyam Bhai to the fullest. There are takers. Number system Class. Alright dear children? previous class We read a very vibrant topic. Classification of Numbers and Reminders Theorem. read off. Today we should read further from him Yes dear friends, the most important thing is I would say divisibility in the number system rules of divisibility what to read Dear friend, yes I will clear your doubt. I will do it whether you are preparing for SSC Are you appearing for Pre Mains or any other Railway exam? Are you preparing for the exam, whether it is police or Prepare for every constable exam. I am asking questions here and this class is for every It is beneficial for competitive exams This is not for any one exam. I'm teaching the number system here. Number system means number of all exams System. Okay kids? From Group D Up to CDS. ok sir let's start Divisibility rules. Divisibility rule of the whole number system The most important topic. And this is only Not only in the number system, further when I tell you I will teach you arithmetic for free. Arithmetic To do quick calculations in questions also go through the calculation process without taking Also to tick the correct answer to the question Divisibility rules help a lot Dear children. Okay, right? So Divisibility rule gives you freedom in body, mind and money. I have to study hard. Is it okay my brother? fun Will come. Let's get started. So look at divisibility, divisibility rule. What does it mean? How do we see the shape of a number? Let me tell you how this number is divided. will be. As we can tell you, this man It is hurt. This seems dishonest. The leader I wore the kurta and became dishonest. such we Can tell the meaning of a number just by looking at it whether this number is from two or from the power of five or By three or by seven or by nine or by 11 or by 13 will be divided by or mixed with these or Will it not divide? These are the questions that arise Brother, in your paper. As soon as you come out of this Not there. This is what you need to know. Isn't it? I I will tell you one by one. You will enjoy it. share Do it. Call him also. both together Sit and read. Okay kids? Read it from afar. Read on a video call Here you go brother. There is no problem. Reading on Is. Ok? Come on friend. First of all, 2 4 8 16 32 or 64 Divisibility rule. You see what this is? These are powers of two. It is a fight between two. Look, give it first. We can take any number By looking at it we can tell that these numbers are two divisible by or not divisible by two Will happen. What are the rules? If a number of The last digit or unit If the digit is divisible by two then the number is divided by two. It will be divided otherwise it will not be divided by two. Like what does two dear children mean? Is? 2 to the power of one. I ask you if this Is the number divisible by two? very large number Is. It takes a lot of time to divide by two. It will take. There is no need. of this number only Look at the last number. The last digit of this number It is eight. Is eight divisible by two? Yes sir It cuts. That means this number is divided by two. Will happen. will be divisible by two. Meaning, if you If you divide the number by two, then On dividing, the reminder will be zero. So If the last digit or unit of a number The digit is divisible by two i.e. the last If the digit is even, divide the number by two. Will happen. Otherwise it will not be divisible by two. Tell me Children, is this number divisible by two? The last digit of this number is seven. What Is seven divided by two? 2 * 3 = 6 does not cut Brother. That means this number is divided by two. It will not happen. That's all I wanted to know. In this You shiver too, child. Good and knowledge I give. If these numbers are exact from two If it is not divided then it means if you If you divide this number by two, you get There will be some remainder after division. Some? Nor will any reminder remain. So you are not like that Divide the whole number by two then the reminder It will come out. No no you are just the last digit seven Divide seven by two. 2 * 3 = 6. What is the remainder? One is gone, that is, even if such a big number If you divide by two, you end up with one. The reminder is about to be saved, did you understand? Dear children, you will say, yes sir, I enjoyed it. This is how we move forward, dear children. When will a number be exactly divisible by four? What does four mean square of two So a number is divisible by four only if When the last two digits of that number are the last two Points are deducted from four. If a number of If the last two digits are divisible by four The number will be divisible by four. Otherwise, not Will happen. Like 7 9 35 88 8 is this number four Does it cut through? The last two digits of this number There are 88 digits. 88 is divided by four 22 times. That is, the number is exactly divisible by four. Will go. Will this number be divisible by four? The last two digits of this number are. 73 It doesn't cut into four. That means this one There is no division by number four. Correct Are you kids? It is recorded. What are you saying? Not recorded son, it is live. Look at it right away The time is 8:30. Don't worry. Okay kids? If this number is divided by four is not divisible means this number There is some remainder when divided by four. Will be saved. So divide this number by four. What will be the remainder after doing this? such for him Not that you divide the whole number by four. Open the whole bundle of things to do. Only the last Divide the two digits of by four. Last of Two two digits are then subtracted from four by 18 * 4 = 72 Will go. What will be the remainder? One. This number When divided by four, there will be a remainder of one. Came fun? Ok? Come like this dear children. Divisibility Rule of Eight. What is eight? 2 to the power of 3 only if a number is divisible by eight If the last three digits of that number are divided into power There are three, right, the last three digits are subtracted from eight. If the last three digits of a number are greater than eight If it is cut, the number will be divisible by eight, otherwise not. Will happen. Like example, everything is an example understand. Does this number cut off from eight? Part It will take time to do it. We run away just like that Can't do it. If you are a child then you can earn this number Look at the last three digits. last three digits Do they cut with eight? 8 * 5 = 40 6 4 8e 64 Yes, this number is divisible by eight. Is this number divisible by eight, brother? The last three digits of this number are 827 827 800 is not cut off by eight. There should not be division, it should not happen at all. It won't happen, right? If this number is less than eight If this number is not divisible by eight then If there is some remainder after division, then Tell me how this number will be divided by eight. If so, will the reminder come, it is not like that You start dividing the whole number by eight. Divide the last three digits by eight. 800 will be deducted from eight, 27 is left so 8*3 = 24 24 is also over, will reminder three remain? Dividing this number by eight leaves a remainder of three. You will understand what 16 16 means. It is 2 to the power of four, so the power of four has come. Now you will make it yourself, my brother, tell me. Not required. A number is divisible by 16 only if will be divisible if its last four digits are divisible by 16 There are divides. are divisible. like so I have given a big number. Is this cut off by 16? Is. Sir, you will tell me to memorize the multiplication table of 16. Give me three days. Then I will tell you that it will be cut No. no its its its you last Look at the four digits. What are the last four digits? Cutting through 16? 16 * 4 of 64 One survived. 16 * 1 = 16 three left. 16 * 2 = 32 this The number will be exactly divided by 16. That's all you have to do. Come forward and make your own stuff. You will take it son. Be expert in setting up. 32 means 2 to the power of 5 then any number is greater than 32 It will be divisible only if its last five digits add up to 32 Will be divided by. Is it or not? so easy The thing is. You keep crying about this. Are? Stop. Let's move ahead. Now five will come What a fight. Whose will come? A fight of five. Five Five is 5 25, which means the square of 5 is 125. That is, the cube of five. any number of Jamure will be divided by five. tell Yes son. How do we find the decay of a number? Seeing the shape that it cuts by five Otherwise you will say, Sir, everyone has bitten me. Is. He also cut me, so I feel like everything gets cut. will be. It's not like that. You have cut it Meaning, everything cannot be reduced by five rupees. You will say, Sir, eight people bit me. this father in law Five won't cut it. so utterly disrespectful our we It's not like that. So brother, any number greater than five It will be divisible only if its last digit Because what does five mean? 5 to the power of one. If its last digit is divisible by five Is. That means the last digit is divisible by five. Needed The last digit must be divisible by five. This means the last digit will be either zero or Then it will be five. Like is this from number five? Does it divide? Yes sir. Five in the last Used to be. Is this number divisible by five? Used to be? Yes, it is happening. tell me is this Will the number be divisible by five? This one 4 966320 Zero at the end, this number is also divisible by five. will be. Will it happen or not? Children, you will say Yes sir. Now I tell you that this tell 89 7328 Is this divisible by five? no sir. Last What is the digit of? Eight. it is divided by five Will not done. So tell him to divide by five. But what will be the remainder? Don't run completely. Just divide eight by five. 5 * 1 = 5 What will come? The remainder will be three. Got it? Bus What does 25 mean just like that? 25 means five Square. A number is divisible by 25 only if When his last two digits are subtracted from 25. Does this number cut off from 25? the last two The score is 25. 25 * 1 = 25 will be deducted. What Can such a big number be deducted from 25? Last of Two digits is 75. It will be cut by 25. Its last Two digits of is 45. 25 won't cut it. Got it? It is 125 125. Cube of five. A number will be divisible by 125 only when its The last three digits are deducted from 125. last three digits Does this cut through 125? 125 * 3 = 375 Yes sir. Listen carefully. Table of 125 Remember. There is homework. 125 * twice = 250 375 * 4 = 500 children? 5 = 625 * 7 875 If you understand 125 8000 then remember that 100 will be deducted. Will this number be subtracted from 125? 525 = 125 Is this number not divisible by 125? It will be so big that when 125 is divided by 12 You are crying, drink water while dividing by 12 How to do the last three digits from 125 125 * 7 = 875 125 * 8 = 1000 i.e. The number will not be divisible by 125, understand it. Understand this much and tell me by asking questions. Which of the following numbers is divisible by 4? + 4 of 13 + 4 of + 4 of 15 completely Which number will divide 3 7 11 and 17 It will divide it among these options. First of all, it is so easy to see the numbers. It's scary. So first, break down the numbers a little bit. Make it beautiful. Take off her makeup first How do you understand? These are 4 to the power 12 13 14 15 so from here 4 to the power 12 everywhere What will come? Common. So what will be left, my love? Children? The power of 4 was 12. 4 12 Common Lay Lia One. 4 to the power of 13 If you take 12 commons, what will be left? Power of 4 1 The power of 4 was 14. 4 to the power of 12 common le Took. So what will be left? Power of 4 Power of 4 2 means the square of 4 is 16. The power of 4 was 15. What did we take in common? 4 to the power of 12 The remainder will be the cube of 4, i.e. 64. so much so that you I could have done it. You will say yes sir. So This is done 4 12 * Yes sir. 64 and 16 80 4 84 1 85 This is it 85. Now tell me that means I wrote this number like this. This number 4 to the power of 12 i.e. it will also be divided by four. Three is not coming anywhere here. from three It will not cut. Isn't it? There are no seven anywhere here. Is. Seven won't cut it. Who will cut this? 17 coming in under 85. Because 85 Meaning 17 * 5 = 85. So this number is 4 Power will be cut from 12, 17 and five Too. So this number is 17 in these four options. Will be divided by. It will happen, right? ok sir. What an easy question you are asking. Let's go here Tell me what will happen quietly? Yes Railway Junior Engineer Exam Pattern 2024 People have questions for you Are. Brother, how many children are engineering? Are you from a background? Yes and no. How many children are engineering students? Tell us by commenting. A six digit number is divisible by 91 Is. If 143 is added to this number, Then the resulting number is which of the following will be divisible by the number? a six-digit The number is exactly divisible by 91. If any number is being deducted from 91 then that number It will be a multiple of 91. Will it happen or not? and if If 143 is added to this number, then one A new number will be created. Tell me who this number is from Will it divide? Tell me by what will this number be divided? someone came Of? Brother, all of them are engineers. Tell me A number is divisible by 91. That means 91 multiple of 91 th something added to it 143 Who will cut this number? You tell me one. 91 It happens 13 * 7 91, I taught it just yesterday. 143 It is 13 * 11, that is, this is 91 times this also is being cut by 13 and 143 is also being cut by 13 Is. So their sum is also less than 13. It will be cut. That means what will be the answer? A. it The number is also being cut from 13. 13 also come in 143 Used to be. So their sum will also be subtracted from 13. Their The difference will also be divisible by 13. So the answer Was 13. This is what I had to do. Come now I I will get it done for you. The first type I gave you taught. four two four eight and five Question on divisibility rule. Come. The selection phase is of graduate level. He is the most Find the largest number which can be divided into seven digits. Substitute p for p in the number 878 93p4 so that the number is divisible by four Could. This is a seven digit number. what is digit Is it son? 0 1 2 3 4 5 6 7 8 9 these 10 digits God gave it to us. Now it has been said here that P Which is the largest number that should be in the place so that the number is divisible by four Go. Now tell me, only then is any number divisible by four It will happen when its last two digits are deducted from four. Isn't it? Now the last two digits are subtracted from four. Needed What value of p should be taken? The biggest. What is the largest digit? nine. If If I replace p with nine, then 94 94 47 * 2 = 94 cannot be divided by four. So the value of P is nine Can't take it. Then what will you take? coming small Are. Eight, what will happen here? 84 84 by four It will be cut. 21 * 4 = 84 so here P What will we hold as the greatest value? Eight. Got it? Any problem? Correct? He is telling everything correctly. Yes. Tell me. Sectional Controller 2025 question. What The maximum value that must be assigned to A that eight digit number is divisible by four? What is the maximum value that should be given to A so that Should it be cut by four? Yes children. This is an eight is the number of digits. What is the maximum for a The value should be given so that it gets deducted from four. Now You tell me, someone will be cut from number four only when The last two points are deducted from four. This is 92 last In. 92 is divided by four 23 times. That means that This number is already being cut from four. whether a Whatever the value, the hour does not matter. it The number coming last is 92. will be cut by four It will be cut. So what do we call a maximum? Can you give value? nine. Because digit What is the maximum? The largest digit nine. Then what is the maximum value of a? nine. Is No? End of discussion. We don't care From this. Because this number has to be cut off from four Have to cut. So this was a fake question. Did you understand? My brother? Come do it. Which of the given numbers is eight? Is it divisible by? Okay kids? which number? All the children who are studying please like Give it to the class. is divisible by eight. Any The numbers are from eight. A number is divisible by eight only if its The last three digits will be deducted from eight. it is 820. Does 820 cut through eight? 800 cuts Will go. 20 won't cut it. 397 is an odd number This will not be cut by eight. 214 200 cuts Will go. Eight to 14 won't cut it. That is, the answer What should come? C option. This is the last three digits 5 6 8 so 8 * 7 = 56 8 * 1 = 8 Last three digits are from eight This number being cut will be divisible by eight. Understand Isn't it dear children? Let go A seven digit number is 8 94 76 Star2. Star is a digit whose value you Don't know. Not known. Minimum of Star What is respect? So that the number is divisible by eight yes. What is the minimum value of star? So that this number is divisible by eight. Tell me It should be non-zero here. what to come Needed? Non-zero. Tell If this number were divisible by eight, then it would be The last three digits of the number are divisible by eight Should be. The last three digits are 6 stars 2 Now what should be put at least in place of star that it becomes divisible by eight. Look, you one You can do it by keeping the option. Isn't it? You You can also put a value here. i you I want to tell you one thing. like in front of you It should be written 600 48 So what does this mean? 600 + 48 Is this what happens or not? don't break it like this Keep giving it. Now like 6 stars are 2 then 600 Separated Lovely Kids and Plus Star 2 Got separated. Correct? You will say yes sir. Tell me dear children that this 600 is eight It will definitely be cut off. Now I have this one here The number has to be taken such that it is divisible by eight. Tell me what should happen? 12 won't cut it, 22 It will not be cut, 32 will be cut by eight. Because What to buy here? Minimum value. So What will be the minimum value of star? Three. Did you understand, children? Yes, non-zero means something. Not there. What will come? Three. Got it? Option You can also try it with this. But look at 12 It will not be cut, 22 will not be cut, 32 is being cut. If you were asked what is the maximum value of a star What will be the value? What is the maximum? If asks for the maximum value, suppose this What is the question, Govind ji? 72 72 comes from 8, so the star will be divided by 8. Let us understand the maximum value of intake. Question See the question of Railway Sub Inspector This is a fair question, just like yours, the maximum of x Find the value Is it okay? The same questions come in every exam. There is no difference. maximum value of x Tell me so that this number is divisible by eight. This number will be divisible by eight only if The last three digits will be deducted from eight. Last has three digits 3x 2 3x2 What is the meaning of x? Maximum value. So Tell me if I replace x with maximum First nine. What is the first digit? Maximum nine. If nine is substituted for x, then 8 * 4 = 32 and 7 2 8 * 9 ends up being 72. Time is up. That is, instead of x What is the maximum you can keep? If you replace x with the maximum digit nine, then It was cut by eight. 8 * 4 = 32 and 7 2 8 9 72 will come to nine. Is it okay my brother? Let go We will start with the maximum. tell me this dear Children, what is the answer to this? An eight digit number is 1 2 3 4 5 6 x y If x is divisible by eight then what is the total of x y Are pairs possible? We If this number is a good question. everything I have compiled it. If this number is divided by eight If it is divisible then tell me Govind ji what is the difference between x and y How many pairs are possible? If this number is divided by eight It is divisible, which means its last The last three digits should be subtracted from eight. The last three digits are there. 6x y asked how many pairs of xy are possible? Now you Look, think about it, should I write 6xy like this? Can I? 600 + xy because that's the point Is. If it is written 654 then how will I write it? 600+ 54 This number 6xy must be divided by eight. So you Tell me, 600 is being deducted from eight. Its Meaning I want to take only xy of this only xy like this That it should be cut by eight. And what is x y? Two Digit number. Is it or not? So one then I x 0 I can take y = 0 because zero is greater than all There is a divide. Isn't it? 600 then cut by eight It will go away. Then what can I write? 0 Eight eight will be subtracted from eight. then 16 then 24 i.e. That's basically the multiplication table of eight. Basically eight How far will the multiplication table go in the end? 96 till. 12 * 8 = 96 This is what I can take x y In place of. Tell me how much is this stuff? of eight I saw the multiplication table 8 * 2 = 16, 8 * 3 = 24, 8 * 12, 12 times the multiplication table of eight. 12 These are numbers and if one becomes 0 then how many Is? So how many pairs of x y will be formed? Yes. Look, he is doing wrong. Hey everyone, swallow him, he is doing wrong Is. Are. Me too Let us go We teach men. But the smokestack is for something as trivial as smoking. Do not take support. We drink water. The intoxication in the water Where is he in the smoke? There is a man in front of us. And men are afraid of meth. Ok? It flutters. Okay kids? I didn't Understand. Son, you will understand. First do a work. Please remember the table Off at. Remember the multiplication table of eight. ok sir? Let's move on, dear friends. Tell me What is the answer to this question? What is the reminder? Tell me. What is a reminder? If seven plus double seven then three times seven, then four times seven, and so on For how many terms is this? Up to 100 terms. This What is the remainder when divided by eight? Tell me children. Very good question. Who Will he? What is the number? once seven then two Times seven. then three times the third number Seven. Four times seven in the fourth number. So The fifth number will contain seven five times. Sixth There will be seven in the number six times. 100 such If you want to take it till the terms then in the last number 100 times will it be seven or not? Ok? 100 times seven. Dividing this by eight Will there be a reminder? Divide this by eight On doing. Okay kids? Tell me. What will be the remainder when dividing by eight? Now It is not that you first calculate this number. When you solve it, you will divide it by eight. Different Divide by eight. When you divide seven by eight If you do this then the remainder will be seven. Only seven will come. When you divide 77 by eight, you get 8 * 9 = 72 What will be the remainder? Five. This is Triple7. We're going to divide triple 7 by eight. what is the remainder Will you come? 8 * 9 = 72 left 57 ie 8 * 7 = 56 That one. Now this is four times intake. have fun right now Did you come? Divide this by eight, dear children. Did. A reminder came. Take this four times Is. And brother, we only need the last three digits. has to be divided. That means if you enter this number If you divide by eight, then only the last three Divide the digit by eight. That means that What reminder will come? One. The next one will be five Times seven. But in the last only three times It is seven. We will divide it by eight. Then what Will there be a reminder? That means whatever number comes next Reminder one when dividing by eight I have to come. Because what does everyone else have in the end? Is? From triple. Now tell me one thing Dear children. What were the numbers? 100. It came to seven. It came to five. 7 5 12 be Gone is the reminder. The two are accounted for. There were 100 numbers. That means how many times will the forest come? Then how much forest Will the bar come? 98 times. Two out of 100 is seven And five became 12. the remaining 1 98 times only then It will be 100. That means 1 + 1 + 1 will appear 98 times. So how much is this? 98 and 12 + 98. Now tell me whether 110 can be obtained by dividing by eight. Is there a reminder? No. Children reminder from eight The elder one has arrived. this 110 back to eight Will bite. I taught it just yesterday. So 13 * 8 = 104 was cut. What will be the remainder? Six. So this What is the beautiful answer to the question? Isn't it? Beautiful Question Tell me. Let's go and enjoy my brother. Let's do it We are ahead. Tell me this What is the answer to this? Yes Are you happy? Six-digit number 4 3 9 x y 5 125 It is divisible. How many such six-digit numbers Are there numbers? Understood dear children? Now Tell me if a number is divisible by 125. Meaning, if the cube of 5 is less than 125 then only will be deducted when its last three digits are less than 125 Cut off means the last three digits x y5 125 If xy5 is to be cut from 125 then xy5 will be such that Cut means the multiplication table of 125 and such It should be that what comes in the end is five. 125 can be kept 125 * 1 = 125 125 * 2 = 250 But what happens in the end if you take 250? Will you go? Zero while what should be? He can't take it. Then 125 * 3 Cannot write 125 * 4 = 500. 125 * 5 = 625 will be deducted from 625 125 and five at the end. 125 * 7 = 800 75 125 * 8 = 1000 So it will be four digits. That means this is If four values ​​are entered at the end, This number will be clearly divided by 125. So that means How many such six digit numbers are there? Why are you telling these three? Hey, why are you saying five? Are? How did you get your five? Are? Brother, please remember the multiplication table of 125 first. It's 375 625 875 so all this from xy5 125 It will be cut, if you keep anything else it will not be cut Only four values ​​are possible, I think. I must have come, let's move ahead now. front next Concept G Next Concept yes, do it Let's do it let's Divisibility rule of 7, 11 and 13 applies to all three There is only one for it. 7, 11, 13 are all prime There is a number. All three are very famous numbers. All three how do we find out if a number is seven is divisible by 11 or 13 No. There is one rule for all three. Easy Going Understand this way. I did so well Many big examples have been taken. I look at I will tell you that this number will be cut by 7, 11, 13 Or not. Listen dear children. This is a number 32396 I ask whether it is from seven or 11 or What is 13 divisible by? Understand Dear children? So there is a way that Simply divide it as you learned. In childhood. The second method is three-digit. Make a pair. What to do? three-digit Make a pair. A pair of three digits. pair It has to be made from the right side. 300 96 this is 32 Only this remained. What should I write if I don't have three digits? Take? What about zero and these? You can get them here dear children. Tell me the difference between them. There will be a difference, there will be a difference of 300 Meaning subtracting the smaller from the larger, 32 from 396 What will we get if we subtract, dear children 300 64 364 Come now, tell me What 364 364 So it has come down lightly, right 364 Divisible by seven 7 * 5 = 35 7 * 2 = 14 Yes, it is divisible by seven. That means that This number will be divisible by seven. Is 364 divisible by 11? 11 * 3 = 33 34 survived. No. This number is divisible by 11. Will not done. Is 364 divisible by 13? Is? From 13. 13 times 26 and 10 is 134, 13 This is also happening. That means this number is even higher than seven. It will be divisible, it will be divisible by 13 also. Butt 11 Will not be divided by. Speak up and understand Did you understand? We You will say, yes sir, if this is the rule then it is for all three Only one rule applies for this and please understand Have patience, a man needs patience in life Tell me, do this first 6 76 962 Which numbers divide this number 7 11 13 So we will make a pair of three digits, one 9 62 one to 676 I want to make it from the right side, will I take these? Tell me their difference, what is their difference? Will you come? Tell me quickly. 676 out of 962 Have to subtract. 67 out of 962 What would you get if you subtracted 2, dear children? How much will it cost, dear children? These six and eight How much will 286 cost? 28 6 This is what's coming. 286 There will be a difference. Understood dear children? Oho Subtract 676 from 962. What will come? 286 Is 286 divisible by seven? 7 * 4 = 28 is not divisible by seven. What Is 286 divisible by 11? 11 * 2 = 22 and 66 Also cut by 11. Correct. From 11 There is a divide. is 286 divisible by 13 It happens? 13 * 2 = 26 two. Since 13 * 2 = 13 It is also divided. This means that this number is which is not divisible by seven but by 11 It will also be divisible by 13. Got the point? So both these numbers 11 and 13 is divisible by but not divisible by seven Will happen. Tell me, did you understand the matter? Tell. Now your mind Sir, I will come here so that the pair is complete. Went. Suppose a seven digit number is It is going to happen, right? Tell me, with whom are these 7, 11, 13? If there is a divide, then see, the rule remains the same. Your three-digit pair will not fail. Make 272 094 and what is this, two zeros after four? Write down 04, three pairs have been formed here, now tell me The problem is which one to add and which one to subtract. So look what you think who is in first place third place fifth Six in the seventh position means odd Coming into position. which comes in odd position If you are in odd positions, you add them. And those who are coming in even position, second, Number four, number six, add them Take it. Their difference has to be taken. understand my Brother? So you tell me, this will come here first. in the third place 272 + 4 276 And how much is this 94, this is their even position What difference will it make, dear children? 182 Is their difference 182? 182 from seven. It is divisible, yes it is divisible by seven. 7 * 2 = 14 7 * 42 is 182 divided by 11 Is 182 divisible by 13? Is it dividing? Yes, from 13 also. Its Meaning this number is such that it is more than seven. It will be divided by 13 also. Divide from Butte 11 It will not happen. Did you understand? Any problem? These Have to do it. Now you tell me this number, this number What is 7 11 13 divisible by? So look, we will make pairs of three. One pair it became. This is it, dear children. Is No? And this became a pair of three. So what Coming in the first position at odds He was added at the third position. add these What is it? 33 33 and the one in even position What is? 33 We will take the difference between these. Difference What is theirs? Their difference is zero and zero It is a number which is made up of seven, 11 and 13. There is a divide. Zero is the most divisible Except for zero. That means this number is greater than seven. It will also be cut, it will also be cut by 11 and also by 13 It will be cut. These numbers are from the three 7, 11, 13 It is divisible. Did you understand these three, children? Tell me the last one 2973402432 You got such a big number, child. Isn't it? Vankhade ji must be understanding. Is this it? Let us tell you. These numbers are different from which of the following among 7 11 13? Is it divisible? Are. 7 11 13 is divisible by Tell me? So here you have a pair of three digits. Will make. 4 3 400 2 900 73 and these two 0 2 are coming in the odd place Yes, we will add them. who comes to even place We will add those that are there. That means two more How much did 402 come? 2 + 402 400 which is even in position in second position in fourth position We will add them. How much is 973 + 432? How much is 1504? 1504 came, right? No. 1505 Okay kids? 3 2 5 7 3 10's 0 and 1 10 Yes 1500 5 ok kids no problem. 3 2 5 7 3 10's zeros and ones 10 405 what Is this baby? 14 5 and this is 14 404 ok my brother no problem If you face any problem, their difference is What will be the difference between 100 and 1001? This is a special number, I will give you a little while. I will tell you now that 1000 is a very famous number. If you multiply 7, 11 and 13, So multiplying all three gives 1001 Learn this. I am special on this Questions also come. I will tell you right now In detail. Okay kids? learn this Take it. That means when I said the difference here I took the position coming on odd and even place of numbers then we will do its difference So 1001 came. 1001 is also divisible by seven Is. It is divisible by 11 and also by 13. This means that this number is so large that It is written for 10 marks. these 7 11 13 There will be an exact division from all three. To understand Did you come, children? I think I understand Is. It was very nice dear Friends. Come. Ok? Yes. Let go. So this is what happened to you dear friends Here the divisibility rule is 7 11 13 Together. Yes sir. Please tell me this. Now 11 is 11. We also give shagun of ₹11. 11 one It is a very famous number. deliberately at 11 There were a lot of questions in the exam. So We also have a special divisibility rule of 11. Will read. Special Divisibility Rule of 11 which Please give your answer quickly. Correct Are you kids? Listen carefully. Let's assume You are given any number. We have this Find out whether this number is divisible by 11. Whether it happens or not, it gets divided. So simple Is. Joe Odd Place Pay Dij Only 11 for 7 Not for 13. which odd place pe digit Those who are coming, add them. Joe Even Place Pay Digits are coming, add them. Joe Even's Place But digits are coming, add them. Joe Odd Add the digits that are coming in place. Then What about their difference? If the difference or So it's either zero or a multiple of 11. Like 11 or 22 or 33 then the number is divisible by 11 It will be divisible otherwise it will not be divisible by 11. Did you understand, dear child? Let go Consider this as an example. These numbers are 1 6 4 5 2 Is this number divisible by 11? So ode Odd means first third fifth seventh position Add those who are coming. even position Meaning those who are coming on the second, fourth, sixth and eighth Yes, add them. So you will add dear Children, what will be the result of adding 1 + 6 + 5? 12. And those who are coming in even position Adding 6 4 10 2 12 gives the odd place. And the digits coming at even places How much is the difference? Difference between 12 and 12 It is zero. If the difference is zero, then this The number 166 452 will be divisible by 11. Did you understand, dear children? Tell me, did you enjoy it? You will say yes sir. Is this from number 11? Does it divide? Please tell me. At the Odd Place Digits are coming, add them. 7 4 11 9 20 8 28 The digits coming in even places 9 5 14 3 17 then what is the difference between 28 and 17 Is? 11 Difference 11 is coming. father of 11 So this means that the number 7 94 5 938 is also 11 It will be exactly divided. I understood Dear children? You will say yes sir, very much Excellent. Let me give you a number By writing. 64 32 7 0 1 Is this number less than 11? Does it divide or not? Tell me quickly. Is this number divisible by 11 or No? Tell me quickly. We What is happening? It shouldn't happen brother. Are? I have to give a new example. 6 3 9 7 16 16 and one 17 and this 4 + 2 6 6 + 6 17 6 The difference of 11 is from the number 11. There will be a divide. Understand my brother? Ok? Me I think you might have understood. Let go Quickly ask a question on this. The question is about the RPF SI 2024 paper. Happened. Don't solve this. Just ask the rules. I want to say that the rules are also in question. Let's go. Which statement is not correct? That means in this All three statements are correct. One is wrong. Ok Children? A number is divisible by five if the The unit digit at the unit place is five of Zero. A number is divisible by five if The ones digit is five or zero. This is correct Is. We did not even study three nine. would have left Are. Didn't even study till class six. Let's see this. A number is divisible by 11 if the sum of Its digit is divisible by 11. This is wrong Is. Isn't it wrong? Any number divisible by 11 If the sum of its digits is divided by 11 It happens. I did not teach. That means this That thing is wrong. Okay kids? So its What will be the answer? D option. it's wrong I had to tell you. You will say, Sir, absolutely right. very nice. Let me first tell you about 11 I would have asked questions on the divisibility rule itself. Am. Isn't it? Only on the divisibility rule of 11 Let's do it. The first question will be correct. Let me tell you. Rule of 11 I read you Gave. 11 of the Special Divisibility Rule Question. Come tell me. I gave you four numbers. asked which number Is it divisible by 11? Divide each one and check Started doing it. You will go crazy. selection phase and Same question came in both NTPC. Beans Tell me whether the number 8 6 is divisible by 11. Sum of digits at even places 14 7 21 and 7 28 We will find the difference between 8 5 13 and 4 28 and 17 11 means this number difference is 11. If the number is multiple of then it is divisible by 11 There is no need to check further Is it correct, will this option come? This number The first one is divisible by 11. Your answer will come. Tell These eight questions of NTPC 12th Level CBT One The number of digits is divisible by 11. So The question is what will be the minimum value of p? Tell me. If this eight digit number is divisible by 11 What will be the value of p if it is divided? Tell me Children. Hen Khede ji. If this number is divisible by 11 If it is divisible then apply the rule of 11. 7 2 9 9 3 12 2 14 and those coming in even place digits Add them 9 4 13 + P and P + then 9 4 13 5 18 + P their difference dear friends this 18 + P has come and one has come your 14 odd and The sum of the digits in the even place is their difference. It should either be zero or a multiple of 11. Now tell me yourself, will this difference ever be zero? Will he be able to come? This is bigger than 14, 18 + p brother. Subtracting 14 from 18 will definitely give you zero. No. That means the difference is not zero. Can. Then what should it be? from zero Big means 11. If I make it 11 So what should we subtract 14 from to get 11? From which number should 14 be subtracted to get 11? So tell me, is your number 25? out of 25 What happens if you subtract 14? 11 So here What value of p will you have to keep then? The value of p will have to be kept at seven. 18 7 25 so The value of p has come, you must have understood this. No problem. Come A six digit number has been given, dear children. 984 m69 It is divisible by 11. So below are Which of the options is between m and n? Can there be a correct possible relation? It is possible Is. Are you children? Tell me dear brother. if these If the number is divisible by 11, then which m and Can there be a correct relation between n? These The question is. Tell me children, what will come? n + 4 + 6 This is the sum of the digits in the odd place. that the sum of n + 10 and the digit at the even place How much is it? 8 + m + means 17 + m 17 + m this will happen dear children if you have any problem Won't you say it, sir? So its difference dear Friends, you should either become zero or 11. multiple of If I multiply this difference by zero I do it, the difference may be zero, so what? Dear children, the difference will come, meaning it will decrease. Let's take this and subtract it from this. Tell me what will be the difference Children will subtract m from n, so n - m is 10 subtract 17 from the minus -7 goes there So what will come out plus so n - m is equal to if If it is 7 then the number will be subtracted from 11. Is n - m 7 visible? This one is visible. A option if n - m 7 Is. If I multiply both sides by minus If I subtract m - n, how much will it be? m- n will come to minus 7, that is, these m and n There may be a possible relation between them. Ok Children? Come next The question has come in UPSC seat 2026. Now look at the CSET paper also. The question came up on rule 11. If x and y are two digits and this number is divisible by 11. x and y are two digits and these numbers are beautiful C is divisible by 11. So asked x + y The remainder on dividing x + y by 11 is 11 What will be the reminder when divided by? If this number is divisible by 11 then What should be done about the digits in the odd and even places? Even Then we differentiate 4 5 9 and 9 4 5 9 18 4 5 ok sorry 4 5 9 7 16 16 + that is What will be the sum of the digits in the 16th even place? Dear children, x + y + 9 means 9 + x + y it is done dear friends you will say yes Yes Sir, now this difference has been made either should it be zero or 11 if I I make the difference zero. Zero possible Is. Yes sir. We will subtract 16 from this 16 and get 0. Will go. If you subtract 16 from 16, you get zero. That is, what should x + y become? because from 16 - 16 0 then what is the value of x + y Is? The value of x + y is seven. Then x + y is divided by 11 If you divide by what will be the reminder? x + y these seven. seven divided by 11 do. Will there be a reminder as well? Ok? Our class is going to get 300 likes. Get 500 likes quickly, my brother. Then You will enjoy it more. It has just begun. Ok? Rest you do or don't do. Your desire Brother, we are interested in teaching. Ok? Nothing else matters. teaching There is no limit to the joy I have. Come on, dear friends. If the number is 54k 31 mm82 There is a white number. is divisible by 11. So It is asked to tell the maximum value of k + m. Look, we have to assume that k and m are digits. Are. What is Digits? digits i.e. k And the value of m should be between 0 and 9. Can. Isn't it? Taking you out of this question is the maximum value of K + M. Ok Children? Tell me it is 23, 13, 12 and 11. See Even 23 cannot be the answer to this question. Can 23 also be the answer to this? Are Children? Two digits can be added to get 18. A big one may come. any digit What is the maximum value? nine. So 9+ Even if it becomes 9, the maximum will be 18 only. The sum of two digits. It can never become 23. That means this can never be the answer. The answer should be from these three. Is No? Younger than 18. Let's say it is divisible by 11. Apply the rule of 11. 5 + k + 1 1 + 8 How much is it? 5 and 1 6 and 8 14 + k Correct Isn't it? What is the sum of the digits at even places? Will you come? 4 3 7 + m + 2 means 4 3 7 2 9 + m 9 + m Okay dear children now this difference is either These should become zero or a multiple of 11. It looks a bit big, if 14 comes here Let's say I make its difference zero. What would happen if I made it 0? 14 - 95 + k - m = So I can also say take it here. - k = m - k = 5 let's move this over to m - k = 5 So m and k can be two digits whose The difference is five. Now there are so many digits Are. Even if one is subtracted from six, the result will be five. Even if you subtract two from seven, you will get five. But There are many cases. We value that I have to take m and k. to get that digit that they The maximum came from the addition. The maximum of the sum is then It will come when m is taken very big. So what can you take then? Look at nine If you subtract four from it, you get five. 9 4 anyway 8 Even after subtracting 3 from it, we get five but 9 8 + 4 is 13 so 8 + 3 is 11 If things are not working out then what if I take m 9 I am yes and I take k four, then its Maximum value is becoming one 13 and see It is also the biggest among the 13 options i.e. There is no need to check the rest. that is No, my brother? Correct? I thought you would understand. This is a very interesting question. Let's move forward Let's go my friend and I will teach you. Please make this. Don't have to make it. I….to you It is said that any number is divisible by 11. It will happen or it will not. I taught you, right? But Very little. Know this knowledge. 1% Even the children do not understand and there is a shortage in the paper too. Comes. I did not tell anyone that Reminder on dividing a number by 11 What will come? A very good trick is in front of you. I am going to open it. If you multiply a number Like someone gave you a number. I this Can I tell you if this number is being cut off by 11? Is it or not? So 4 2 6 and 5 6 And the difference of 11 is five. That means this number It will not be divisible by 11. From the number 11 There will be no division. if not divisible by 11 If it happens then you will divide it by 11 then it will be a reminder What will come? I'm teaching you that reminder. Am. On dividing a number by 11 How do I remove a reminder? are the children Listen. There is also a very good way to that any number when divided by 11 How will you remove the reminder? Is Children? Please tell me. Have to start from the right side. Keep decreasing. 6 Subtract 2 from four and 4 from five One more, add these up, 1 + 4 5, these reminders You will have to divide it by 11 and see Reminder five will come only 11 * 4 = 44 a 12 11 * 1 = 11 How much is left 11 * 1 = 11 Reminder five whether children understand Look, this is what we get when we divide it by 11. Will there be a reminder? 4 - 7 - 3 - 8 - 5 or 6 So 0 6 - 0 6 we will add 6 and minus That is, on dividing minus by 11 It came negative. You got minus, right? So if If we ever get a minus, who are we running from? Are? Doing it from part 11. If negative If it goes then add 11. We are dividing by 11. Yes, add 11. That means nine. -2 in We will add 11 to nine. So nine reminders will come. You Divide this by 11 and you will get a remainder of nine. Is it or not? This is a great thing Wankhede ji Tell me such a large number that it is divided by 11 What will be the remainder after doing this? 6 - 1 2 - 0 2 3 - 7 - 4 4 - 5 - 1 Add these together Add dear children -5 and -5 end What reminder will come? You can dial this number from 11. Divide by two and see if you get a remainder. ok friends let's have fun Now I have very few questions on this but Whatever it is, you should do it. Tell me dear children We make Rani Kumari is saying will you complete the I will complete the entire class, Rani Miss, I want to ask if you are completely will you be able to read When will the RRB NTPC Under Graduate exam be held? Will you come brother? You make my day 40 hours long Give. The day my day became 40 hours long No, the goods will arrive on the same day within 24 hours. Why Is this amazing sir? You should know this Needed Come on kids, tell me what the smallest number is. Which one is that you should add to it and see What number is given that is the smallest What is the number that can be added to this number? If given then the number obtained is less than 11 It will be divisible. This means that this number is currently 11. It does not divide. What am I like in this Let me add it so that it is divisible by 11. So First you find out how to divide this number by 11. What comes as a reminder when divided. First you have to find out whether this number What will be the remainder if I divide by 11? So subtract 2 from 6, you get four. 6 - 1 5 - 3 2 4 - 5 minus 1 and 4 minus 9 Five minus five was deducted. 4 2 6 - 1 5 i.e. That reminder five has arrived. So I can say If you divide this number by 11 So the remainder is five. what would be left Is? Five. Five survive. what added Should I go? It should be added so that this number is subtracted from 11. The remainder when this number is divided by 11 Five survive. If I subtract five from this Even if I give it, the number will still be deducted from 11. Is No? I told you one method yesterday. second that If the remainder after dividing by 11 is five. If I add six to it, what is 5 + 6? Will be done? 11 is still subtracted from the number 11 Will go. So what should be added to it? Six Isn't it? On dividing this number by 11 The remainder is five. If six is ​​added to this number It should be done. If you add six to the reminder 5 + 6 will be subtracted from 11 11. complete The reminder will be zero. So this number is less than 11 It will be cut. So what is there in it, dear? Children should add g. Okay kids? With this the type ends. Correct Are you kids? Let me ask one more question I. Tell me the next type, dear children. This is a question from the CDS 2023 paper and I Really hope that something like this happens in SSC too. There should be vibrant content. Make it children. If this number is divisible by 13. With whom? 11 is over. Whose system will it be now? Used to be? Of 13. If this number is divisible by 13 If it is divisible then what will be the value of p? somewhere p will be missing. Here it is, p, right? The value of P What will happen? Tell me Sonu Bhai. Yes Tell me The child is studying. He reads with his heart. If this number is divisible by 13 then the value of p is What will happen? Brother, I followed the rule of 13. I have taught. This number is divisible by 13. So tell me 13 What is the rule of? Three-digit pair Make. So a pair of three digits was formed today. Let's take it. Whatever happens will be seen. 38 7 75 9 83 P 13 2 and Ye00 These are the four who are in odd play positions. Will add it. What is the odd position? 04 83P And 38 7 is that it, isn't it, kids? 387 then tell me the sum How much will it cost? 387 + 4 what happened? 390 391 + 83 p These are the numbers in the odd place that I have I added them and those who are at even places Add them up in the place, 132 and 75 is 9. No 132 and 759, tell me what do they add up to? will come Adding 132 759 gives them 81 91 If this number is divisible by 13 then what is its The difference should be deducted from 13. Their What difference should there be? The one to be cut from 13. This is a dangerous question. For normal children Question for men. here you from here We will make pairs of three dits each. 38 759 83p132 4 right? Which is in odd position, first position I added them on the first, third and fifth. Who They were added at even position. what about them Will you take it? Difference. Now you tell me, this three looks so big. Used to be. 800 + 300 is what looks big. So difference means subtract this. Tell me 391 891 out of 100 is easily decreasing. What will come? subtract 891 from 391 minus What will be the result if we subtract 500 from 83p? If we subtract 500 from 83p, we get 33 3p Will not come. Brother, let's say it is 838. 500 Subtract. What will come? Is it 338 or not, children? So this comes to 33p, this value should be like this that it is exactly divisible by 13 because it The number is divided by 13. Now tell me what you have Let's replace p and cut it by 13. So 13 * 2 = 26 13 * 2 = 26 How much is left? 13 * 2 = 26 If seven is left then 7 13 6 78 That means what should be put in place of p? If If you replace P with eight, the number becomes 13. It will be cut. 13 * 2 = 26 and 7 8 13 * 6 = 78 Okay kids? So what will be the answer to this question? Of? Tell me eight. Isn't it cool? Ok? I have asked this question of 13. Beans Even if the question was made on question seven, the same method would have been followed. Would. If it is made at seven, right kids? So There is no point in getting two of them done. Ok? I think you might have learned it or not. So yours is just some junk almond Keep eating. Munkha understand? Yes. Well, that was great. Are you having fun kids? If you like the content, please comment once. Tell me, write it down once, do you understand? I am enjoying reading it, I like the content My teaching method is coming Explanation: Are you enjoying? 33 P Bhaiya, I had to subtract 500, but it did not even subtract. Get it friend Brother, the child did not understand 33P should I leave it Look again, brother, okay, let's move on. Now the number system will appear before you. The most dangerous point Divisibility rule of three and nine. three and nine Great reading of the divisibility rule. great fun Will come. Divisibility rule of three and nine. nine Nine is the most beautiful number in the world For calculation. who commanded the nine Lee, accept that. Suppose half Arithmetic work has become easier, calculation Of. So, you have to understand it very well. three more nine. Okay kids? When will a number be divisible by three? If The sum of the digits of a number is If the even digit is divisible by three then the number It will be divided by three. Otherwise divide by three It will not happen. Did everyone understand what I said? If The sum of the digits of a number is divisible by three If so, the number will be divisible by three. Otherwise, three Will not run away from. like for example This number is 750369 This is the number. Is this number divisible by three? Is? So I'm going to divide by three like this. No. Isn't it kids? The sum of its digits Take it out. 7 5 12 + 0 12 3 15 15 6 21 and 9 30 The sum of its digits is 30. and 30 which is It is divided by three exactly 10 times. i.e That this number will be divisible by three. That's it There is a rule. Any problem? Similarly, the rule of nine. A number is divisible by nine if The sum of its digits is divisible by nine. If the sum of the digits of a number is greater than nine If division occurs then the number will be divisible by nine. Otherwise it will not be divisible by nine. The Rule of Nine Is. If the sum of the digits of a number is nine If it is divided by then the number will be divisible by nine. Otherwise it will not be divisible by nine. like what Does it intersect with number nine? The sum of its digits Take it out. 5 7 12 6 18 9 27 of its digits The sum is 27. 27 is divided by nine. What does it mean This number will also be divisible by nine. from nine There will be a divide. Is this number divisible by nine? will be? 7 and a 8 5 13 1 14 4 18 this number The sum of the digits of is 18. This means that The number will also be divisible by nine. 18 is cut by nine If so, then the number will also be divisible by nine. Ok No? Is this number divisible by nine? so like this So it is not that I will divide by nine. Its Find the sum of the numbers, dear children. Its What is the sum of the digits? Tell me my brother. 3 5 8 6 14 4 18 6 24 8 32 7 39 48 and 2 50 Then the sum of the digits of this number is 50. The sum of the digits of this number is 50 and 50 is not divisible by nine. This means that The number given will not be divisible by nine. To understand Came? This number will not be divisible by nine at all. Keep doing whatever you want. Obviously, if this number is divided by nine If it is not there then on dividing it by nine Some residue will remain. So it is not that You have to work hard to find the remainder. Have to do it. You have added the digits of this number. Took out 50. 50 doesn't cut it with nine. These The number will not be divisible by nine. So this If the number is divided by nine, then What will be the remainder when divided by nine? So What is the sum of the digits of this number only? 50. Now divide 50 by nine. 9 * 5 = 45 What reminder will come? Five. That means I am I can find out that if this number is divided by nine If divided by then the remainder is five. Will come. No problem, you won't say anything, sir. There is no problem either. It is an important matter If a number is divisible by nine then Three is the child of nine, so the number It will also be automatically divided by three. So What is the real thing? nine. Nine, got it? So three It will happen automatically. Did you understand, dear? Children? So we have to concentrate completely on nine. Nine is the magic number in the world of calculations. And I will go into this for you in depth. I will explain why it is so that for a number If the sum of the digits is less than nine then only it The number will be deducted from nine. Did you understand? With love Please understand. You will have a lot of fun, dear children. Let the four digit number be ABC. D. Suppose a is a four digit number a b CD. I ask you to divide A B C D into nine What will be the remainder when divided by? Number A Divide B C D by nine. What is the plan? Divide the numbers A B C D by nine. So here This is a four digit number. D units digit Is. C is the tens digit. B. Hundreds place There are marks. This is the digit in the thousandth place. Just like that is the 1000 place digit. So what should I write? D in multiplied by one, in C multiplied by 10, in B Multiply by 100 and multiply by 1000 in A. This way It is written. It is written like this. So this is it 1000 a + 100b + 10c + d if it is divided by nine Who will we run away from? From no. So you tell me from nine If you are dividing, the thing that is subtracted from nine Cut that out. This is 1000 a. What 1000 a I can write 9a + a like this Am. 9a + 1000a is This is in front of you 100 B. 100b can be written as 99b + b It happens that 100b is in front of you and 10 is in front of you. There is 10C in front, I can write 10C like this hmm 9c + I broke it down and wrote it down Problem 1000 a to 9a + a 100 b to 99 b + b 10c to 9c + c when you see this dear Children, this number, this number, All these numbers are multiples of nine. Nine is a multiple of nine. Triple 9 also from nine It is deducted from 99 as well as from nine. That is, if If I divide it by nine, then nine will be exactly It will be divided. So what's left? Only Your remaining a + b + c + d means you only have Same a + b + c + d divided by nine Have to do it. And what do you get when you divide by nine? Will you go? The reminder will come, dear children. And what is a + b + c + d? of the number The sum of all four digits. What is? of the number The sum of all four digits. So brother, I had four The number of digits was taken and the rule was made that When I multiply this four digit number by nine I am running away. So if only this number Sum of digits divided by nine If you do this, you will get a reminder when you divide by nine. Will go. If the sum of the digits of this number i.e. If the sum of the digits of this number is divided by nine If it goes then it means this number is also complete nine. It will be divided by and what is this? of nine Rule. The divisibility rule of nine was fun. No? So it had to be understood very deeply. Here This proves that if a number The sum of the even digits of the number is less than nine. If so, the number will be deducted from nine. It does not cut So brother, divide the sum of the digits by nine. Take. The reminder will come. Did you understand? You Sir, you will understand it very well. I came. Now let's move on to the next concept All the children will put headings in their copies. digital sum digital sum digital sum Listen, you will enjoy it. What is digital sum? There are a lot of numbers in the world. Every number You can divide by nine. any The remainder when a number is divided by nine All that remains is the digital equivalent of that number. They say. Dividing any number by nine The reminder that remains after doing this can be saved in that It is called the digital sum of the number. Let's assume You have a number n I can multiply this number by I divide by nine. on dividing by nine Some reminder or the other, i.e., remainder will remain. The same reminder will be called n of number n The digital sum of which is spoken in short Did you understand what ds is said, children? So dividing any number by nine gives The remainder is the digital equivalent of that number. It is called equal. You understand what I'm saying You will say, yes sir, I understand. Such as Let me write 65 in front of you. If you are nine on 65 What is the remainder if you divide by? 9 * 7 = 63 is the remainder. When you divide 65 by nine If we do this, the remainder comes out to be two. So what about 65 The digital sum is 65 which is the digital sum Dear children, what is that? Two. 65's The digital sum is two. I understand dear Children? Isn't it? So any number can be divided by nine The remainder left after dividing by is the same as that is called the digital sum of the number. good a Tell me if you divide a number by nine If you are dividing by nine, the remainder will be nine. will come smaller than. That is 0 1 2 3 4 5 6 7 8 Nothing older than nine will come, dear children. Hence the digital sum of any number is always It is a single digit number only. The digital sum of any number is always one. It is a single digit number. forever one It is a single digit number. Do you Did you understand what I said? You will say yes Sir. Correct. very well understood I came. Did you enjoy it? You will say a lot, sir. Excellent. Digital sum is a very important thing. digital What does sam mean? dividing a number by nine garbage, trash, junk, donkey, anything Is. Divide by nine and what is the remainder? Is? His digital sum. I just explained If a number is divided by nine, If you want to know the reminder then you can enter that number. Divide the sum of the digits by nine. So the numbers If you divide the sum by nine, then The reminder will come. Did you understand, children? You You will say yes sir. Now let's be careful Hear I took an example in front of you. this one 3 5 6 4 6 8 7 9 2 this this I understand it very deeply. of this number What is the sum of the digits? 50. That is, the number It is not divisible by nine. You divide this by nine What will be the remainder when divided by nine? Will you come? Five. That means I know this What is the digital sum of the number? This which I gave an example of this number in digital form. Even is five. because this number is divided by nine remainder after division The remainder when divided by nine is five. digital To find even or to divide by nine It is not necessary to remove a reminder. You must add the digits of the number completely. Please listen. What do we have to do? I know What is the digital sum of this number? The remainder when this number is divided by nine What will come? So what should I do? This number I will add the digits of. digits of this number What will happen if we add this? 3 + 5 3 + 5 + That's 6 + 4, right? What else? 6 + 8 6 + 8 + 7 + 9 + 2 is the sum of the digits of this number. What is? This is the sum of the digits of this number. What I know is coming? 50 The sum of the digits of this number is. the same number Dear children, I need to know the sum of the digits of What is the plan? Have to divide by nine. This The sum of the digits of the number is divided by nine Have to do it. And when I divide by nine So think for yourself what is being cut by nine Cut it before that. The thing that is cut by nine Like 3 + 6 is 9, so complete it with nine. There will be complete division. such that 5 + 4 is 9 If it is left then it is completely divisible by nine Will go. Like if it is nine then it is complete with nine. It will be cut. Like 7 + 2 equals 9, complete by nine. What is left completely? 6 + 8 6 + 8 14 6 + 8 What happens when you divide 14 by nine? Will there be a remainder? Will five come or not? Tell me the reminder. Yes or no? Any problem? Is it or not? This means you have to add the numbers. There is no need for it. Where nine cut me Divide by nine. The one who is cut off from nine gets it first Just cut it. What is left? digital Even. What is left? Digital Sam. Came fun? I enjoyed it. That means I should remove it. As There is a number. I need to find this number What will be the reminder when dividing by nine? What is its digital sum? So keep removing nine. Keep removing nine. 3 + 6 9 I will cut your throat. 5+ 4 9 I will cut your throat. 7 + 2 9 will cross out nine I will cut off what is left of six and eight six and eight Add the numbers 6 + 8 14 brother divided by nine If you do this, you will get 14, but the digits of 14 will not come. Add again 1 + 4 five i.e. digital What is even? Keep adding five until Keep adding until you get a single digit. Until a single digit comes to mind I enjoyed it my brother, will you say yes sir? This is the digital equivalent, boy, memorize it like a donkey. So he takes it, but I think today he You must have understood, dear brother, this digital sum are we These numbers are given in front of you. Me Tell the digital sum of all these numbers In short, what is DS? i.e what do you get when you divide these numbers by nine What will be the remainder? This has to be found out. So one then The method is to add the digits of the numbers. Then Divide by nine. Will come. Hey brother, to do No need. Cut out the point where nine is being formed. 8 + 1 9 2 7 6 3 left 5 + 0 5 + 0 5 this The digital sum of the number is five. From this nine Try dividing and the remainder will be five only. See here for your digital sum. Is. Are you having fun kids? Please like it. 5 4 9 6 3 7 2 0 + 1 Digital of this number There is only one. 3 6 2 7 8 1 What's left? this is You guys have written the same thing, friend. Are? Let's remove this. tell me what is its digital equivalent Is? 6 3 9 1 8 2 7 4 The sum of the digits of this number Its digital sum will be eight. Tell me, I will do it. Find the digital sum of any number. As long as you can, you can see all the nine that are there. Keep removing and adding until one Single digit should not come. Single Digit Ani because dividing by nine reminds It will be in single digit only. Tell me this is it Digital Sum Concept. You will say yes sir. Now you will say Sir It's digital, brother. of digital sum What is the use? Isn't it true that children are digitally What is the use of? listen carefully Dear children. All children, listen to me carefully. Very You will enjoy it. Yes Digital sum zero or digital sum nine or one That's it. If the digital sum of a number Whether I say zero or nine, it's the same thing. The thing is. Dear children. Look, I'm someone I divide the number by nine. If the number by nine, number by nine If it is completely cut, what reminder will come? If I say divide by nine If reminder nine is coming after doing this then its Meaning nine is also the last reminder of the cut from nine. It is just zero. Then the digital sum of a number Should it be called zero or digital sum nine? It's the same thing. You will say, Sir, I did not understand. For example, suppose I am standing in front of you I write the number. Dear children, 72 me What is the remainder when 72 is divided by nine? Will you come? So 9 * 8 = 72 remainder will be 0 so 72 When divided by nine, the remainder is zero. Is. So what is the digital sum of 72? of 72 The digital sum is 0. But if the score of 72 If added, what will be the sum of the digits of 72 Are you coming? 7 + 2 7 + 2 9 is the same thing. Therefore, we can say that any number Whether it is digital sum zero or digital sum nine. One That's it, dear children. It means no The number will be divisible by nine only then. any number It will be divisible by nine only if its digital sum is Either zero or any number greater than nine will be divisible when its digital sum is zero or Be nine. Like I have put the number in front of you. Had taken. Is this number divisible by nine? Used to be? So you find its digital sum. So Find the digital sum 5 4 over 7 2 9 what The remaining zero is the digital sum of this number. This means the number is divisible by nine. Did you understand, dear children, then there is no number It will be divisible by nine only if its digital sum is Is it nine or zero, I understand the digital sum Zero or nine is the same thing next Any number in the world has a number, right? Does it mean it is an integer or it can be in decimal also? Can children divide any number by nine? On dividing by digital sum we get a number When multiplied by nine, the digital sum is always nine. Will come. If you multiply any number by nine If you multiply, the number will be a multiple of nine That is, subtracting from nine and if any number If it is divided by nine, then it means that number What should the digital sum be? There should be nine Or it should be zero. to any number If you multiply by nine, the number you get will always be Its digital sum will be nine. Let's say 17 Is. 17 is a number. 17 multiplied by nine What will happen if you do it? 17 * 9 100 of 153 What is digital sum? 1 5 6 3 9 226 * 9 is. A number is 226. nine of 226 Multiplying in. 2034 comes. of 2034 What is the sum of the digits? 2 + 35 49 9 digital What is even? There is a number 114.8 Multiply this by nine. You will say Sir point come Went. Don't be afraid of points. When I tell you I say if it was 1114.8 * 9 then it would be 1148 There is multiplication in nine. the decimal would just be set Is. Isn't it? So don't be afraid of decimals. Calculations are done in digits only. Numbers Calculations take place in this only. decimal then Sets at the back. So we will multiply. Multiplication I will come only after doing it. Look at the sum of its digits. 1 3 4 3 7 2 If any number is divisible by nine If we multiply, the digital equivalent of the result will be There will always be nine. You will speak so deeply, sir. If we had known this, we too would have been cheetahs. Ok? No problem, I will make you grow a moustache, you will become a leopard. Listen carefully. In any calculation If that is not approximate but exact calculation Is. You must have noticed that we often ask questions If yes, then it is written up to two decimal places. Tell me the approximate answer. Almost not. If we any Exact calculations are being done around the world A left-hand side in any calculation It's going on. A right hand side is going on. Always the digital sum right of the left hand side Equals the digital sum of the hand side. This is the left hand side, right hand side. Digital sum means the left hand side is also divided by nine Divide by. The right hand side is also cut off by nine Run away. If both sides are equal then nine remainder on dividing by or dividing by nine But will the digital sum be equal or not? So In any calculation, the left hand side and Right hand side digital sum always matches Should be. If there is no match then calculation It is wrong. Look, multiply 4 5 67 * 615, that's it. The bandage will come. I did this on my own will I have taken an example. left hand side Find the digital sum. 4 5 6 7 13 13 digits Reconnect it. Add 1 + 3 until Until it reaches single digit. 6 and a 7 5 12 Will add the marks again. 1 + 2 then Its digital sum is then 4*3 = 12 If we add the digits of even 12 again, then three The digital sum on the left hand side is three We will calculate the right hand side 2 7 8 16 5 Sum of the digits on the right side is 21 21 What is digital even? Did you like it? It's fun. Children Try adding 22 * ​​17 and it gives 374. Its digital sum is 2 + 2 1 of 17 + 7 8 4 8e Add the digits of 32 32 again 3 + 2 So its digital sum is five on the right side. Three and seven 10 4 Sum of digits of 14 again 1 + 4 digital Tell me whether the even number five came or not. Any calculation square addition subtraction Multiply anything 125 squared 25 is 15625 Remember the digital sum on the left hand side? It is the same as the right hand side, try it and see. What is the digital sum of 125? 1 2 3 and five one two three five eight square of eight 64 Sum of the digits of 6 4 10 Digital Sum of Left Hand Side and Right Just calculate the hand side 6 2 8 1 9 five and the sum of five 10s on the right hand side The side details are all the same too. Let's not come Children, come to our class to know about Bihar After this the children understood that this happened, it is okay. Now Tell me dear children, how big are they? If calculation comes in front of you, you can ask questions. What are you doing. All this calculation remains, right? So how do you do such huge calculations? Masterva does everything quickly? because ugh Digital knows even. Are you kids? Digital Sum With the help of this you can earn at least £100 without any calculations. You can find the answer in less time. For example, suppose you have to cube 83. 83 What is the cube of equal to? you do not know. No Do you know? I don't remember either. either Will have to remove it. And you have four options. Is. There are four options in front of you. And we are 83. Don't want to remove the cube. So what will you do? Dear children? Now calculate the digital sum. which is 83 cubes Digital is the same as the right answer is also digital There should be an even match. That should be the match No? You will say yes sir 83 means 8 + 3 is 11 means eight. Add three 11 11 digits Take. Two. The cube of two is eight. That is, 83 It is a cube. The digital sum will be eight. Eight will come Digital Sam. So the correct answer will be the one which Digital sum eight will be formed. Which one is it brother? 1 + 8 5 7 12 and 6 18 5 7 12 6 18 is also nine Went. 1 8 9 means its digital time is seven Which is wrong. There should be eight matches. Here we will see another eight Then the digits 7 21 21 and 5 26 26 Add 2 + 6, its digital sum is eight. Option number is matching Here we will see 5 10 8 18 9 becomes 7 14 and one six what has come of this six digital sum has come Dear children who are not eight, that is. This one is wrong, look at this How much is three seven 7 10 8? nine. 3 7 10 8 18 is nine. Cut by nine. Remove it. 7 14 5 7 14 5 19 Also remove nine from 19. Is its digital equivalent left? One means that this There will be no answer either. There is only one option which Digital Sum Eight is being made. B this one The answer will be. Did you enjoy it? Let me tell you. This What is the correct answer to the question? This calculation What is the value of? Please correct it. We tell me please Everyone's C came. very nice. C is coming Nor everyone's? Let me believe you, I can Pay? very nice. I learned it. there should be applause I want it in your honor. C option is absolutely You are right. Now let me tell you this I ask questions based on this. well carefully Please listen. Like I did nine very well I explained it. If you understand nine then three will also come. What does the rule of three say? any number three will be divisible by only when the sum of its digits That means the digital sum is divided by three. Any A number is divisible by three only if its The sum of the digits i.e. digital sum of three Cut. Digital sum to be cut off by three Needed The one that cuts through three means digital The even must be either zero or three or six or nine. If the digital sum of a number is 0 3 6 Or if nine comes then it means that number It will be divided by three. Any number greater than nine Divided when the digital sum is either nine or Zero. It's the same thing, nine or zero. like now This is the number. I ask you to find this number Is this number divisible by three? either You can add up its digits or What to remove directly digital sum 3 6 9 7 and Sum of five 12-digit numbers The sum is three, that is, the digital sum of this number. If it is three, then it is obvious that this number is three. It will be divided, understand dear children If it is clear then here it is only for digital sum Come now dear children, we have to apply the concept. I explained it to you 2 5 3 7 11 9 all explained But sometimes questions come in the paper Large numbers are based on these On the divisibility rule of. like suppose Let me ask you the divisibility rule of six What is? When a number is divisible by six Will it happen? So I taught you the rule of six. No. Didn't you teach me? Have you read it? I Let me ask you when a number is divisible by six Will it happen? Tell. So I can write six like this. 2 * 3 How are two and three? are coprime to each other. Co-primes two and three have nothing in common Is. If a number is divisible by two and is also divisible by three. Its Meaning that number will also be divisible by six. The rule of six was formed. know two and three yes. When will a number be divisible by 12? 12 means 3 * 4 12 three and four together So if a number is divisible by three If the number is divisible by four then that number is divisible by 12. will also be divided. Now some kid started saying this Sir, I will write 12 like this, means 6 * 2 = 12 Sir, if a number is divided by six and two If it gets cut by 12, it will get cut by 12 also. six and two The number 18, which is cut by both, is also cut by six. Used to be. It is also being cut by two. But what 18 is being cut by 12? No This did not happen because six and two are not equal being coprime and not coprime Needed If a number is divisible by six and If it is being deducted by two then brother it is six and two The LCM is six. That number is from six It will be deducted from the guarantee. Did you understand, dear children? Come on, you have to break it in coprime itself. Understand my brother? 56 Now some child thinks 56 = 4 * 14 that is, if any number is divided by four If it is cut by 14, it will be cut by 56 also. So this It is wrong. You have to write 56. 7 * 8 = if A number is divisible by seven. seven more Eight are coprime to each other. If any number It is divisible by seven and also by eight, so 56 It will also be cut from. Haven't read the rule of 72 72. What is 72? 8 Name 9 If any number Divisible by both eight and nine is 72 It will also be cut from. 9 * 11 for 99 such if Any number divisible by nine is also divisible by 11 It will also be divisible by 99. you are someone's Rules can also be made like this. Got it? Let go Now we will do interesting questions about three and nine. On divisibility rule. Come do it Which one nobody. OK tell. Which of the following statements is correct? Four Gave statements. Intelligence Bureau papers This is a question of. Isn't it? be an intelligent man If you are a child then tell me a number is divisible By 125 if the last three of the number last Three digits of number form a number that is Any number divisible by 5 cubes by 125 It will be divisible only if its last three The digits form a number such that 5 cubed is 5 Cube means it is divisible by 125. it The thing said is absolutely correct. First thing absolutely no A number is divisible by 125 only if its The last three digits are also cubed by five, i.e. That it was cut by 125. So what will happen? Well first. Let's check the second one. If a Number is divisible by two numbers than it is Divisible by the product of two numbers. If If a number is divisible by two numbers then She will also be divided by their product. If a number is divisible by two numbers So there will be a divide from their product also. What Is this true? Is such a symbol correct? If a number is divisible by two numbers If it is different then is it different from their product? Will it also be divided? This is not necessary. I just explained it Suppose you take a number six. Two. If a number is divisible by both six and two It's like it's not necessary that she is 18. Also cut from the product 6 * 2 = 12. It is then that If two numbers are coprime to each other. Associate are prime. coprime if any number are different coprime numbers to each other If they were divided then their product also There will be a divide. but not coprime here I have told you so. Therefore this is wrong. Third A A number is divisible by 36 if the number is Divisible by 4, 6 and 12. Any number 36 It will be divisible by only if it is divisible by 4, 6 and 12 Cut. 24 is subtracted from 4, 6 and 12. What Does 24 intersect 36? No. That means the matter also This is the rule of 36. What will you write for 36? Have to break in coprime. If four names Any number divisible by four is nine If it is also divisible by then only it is divisible by 36 Will happen. Did you understand, my brother? So that means this What is in question? Only First Only Correct Is. Is it okay kids? Let's go Wankhede ji We fulfill your wish. This was the question Of RPF SI. ok baby Which statement is not correct? The first statement is It was right. A number is divisible by five only if When its last digit is either five or Zero. Look at this statement. A number is Divisible by three and not if the sum of digits Is divisible by three and not respectfully. That's correct. A number may be greater than or equal to three or nine will be divided when the sum of its digits is respectively Divide by three and nine. so the thing Wasn't it right? A number is divisible by six. If sum of its digits is divisible by 3 and the The digit at the ones place is any one digit. It increased a lot. very nice. Look at any number When will it be divisible by six? Six means 3 * 2ni. A number is divisible by six only if It will happen when it is divided by three and also by two. Cut. And a number will be divisible by three only if The sum of his marks is divided by three. And someone else A number is divided by two only when its unit's value is What is the digit in the unit place? yes? Be even. So, this means that only The last thing is wrong. The one with 11 is correct, right? Children? So I will not leave anything. Perfect hair We will remove the skin. There are hairs from the skin So when did you leave? Tell me this. Let go This is a question of Group D. today group d question Let me take it for you. an eight-digit number is divisible by 45. If the digit is Rearranged. The digits should be rearranged. Ahead Digitized at the back. Then the number must B. Divisible by. So the new number will be Will it always be divisible by whom? Tell. From 45, By three, by 15 or by five? from the option I have to tell you this only. An eight digit number is divisible by 45 It is divisible. If its digits are flipped back and forth If given, a new number will be generated. that number From whom will it be divisible? Watch Kids From 45 Being divisible means being divisible by more than five. will cut and If a number is divisible by 45, its Meaning that number will be divided by five also and if If the number is cut off by five, what will happen at the end? Will you come? Five or zero. If I rearrange I will give it, I will move it back and forth. It is possible Five did not come in the last. So there is no guarantee that number is divided by 45 or 15 or five Only cut. That means what should be the answer? Use your brain. If a number is divisible by 45 then The number will also be divisible by nine. if anyone The number is divisible by nine because 45 Only nine are left. If a number is greater than nine If it is divided then the sum of the digits of this number The sum of the digits will also be subtracted from three. And me If I switch the digits of a number forward or backward Yoga will still remain the same. beside his wife If the wife is beside the husband or husband, then it is the same Couples understand children? So that means dear Children should write the digits of the number here. The sum of the digits of the number remains the same even after rearranging It will remain the same. So the number will always be divided by nine. Keep doing anything while you do it. and if it is divided by nine then nine is a factor of. It's always three, isn't it? Good question. Would you have understood this? Are? Let us tell you the question of RPF SI. If the number is completely divisible by three and a is the smallest positive integer a which is the smallest positive integer. So to you The question is find the value of a - 2, a - 1, asked a, a + 1, a + 2, a + 3, a + 4 Is. This question will be solved only when you have a The value of will be known. without the value of a then It will not come out. Tell. Brother, if this number is divisible by three. Is Wankhede ji? Then the sum of its digits is that the digital sum also has to be divisible by three Needed Is it or not? You will remove it The digital sum will be 9 3 + 6 9 8 + 1 The digital sum is 4 + 2 6 becomes 4 + 2 6 and One digit left over a 4 + 2 becomes 6 + This is digital even. Is it okay kids? of a Let us assume that this digital sum is greater than three Cut. So I can take the value of a to be 0. 6+ 0 6 + 0 6 will be cut by three. But a said If it should be positive then zero then positive If not, then I cannot take the value of a as 0. Then what if I take the value of a as three If I take 6 + 3 then 9 becomes digital even nine Even then this number is divisible by three because If a number is divisible by nine, then it is divisible by three. It will also be cut, children So here the value of a is three, isn't it? You put this value here instead of a, three 3 - 2 1 3 - 1 two 3 + 1 4 3 + 2 5 3 + 3 6 3 + 4 seven Now tell me what you get by multiplying these. is this Ok The number subtracted from seven will be 5 This is what I'm getting, right, 540, okay kids. Everything seems to be very easy to understand The talk was that multiples of seven will do this next. Question What is the maximum value that must be b is assigned to a so that the eight-digit number is Divisible by three. This is an eight-digit There is a number. It is missing one digit. The name is a. The question is what is the value of a? Should it be? The maximum value so that three Get cut off from. What should be the maximum value of a Should it be cut by three? It will be divided by three only if its digital sum is three. Cut from. Then you calculate its digital equivalent. Dear children. If we take out the digital sum then it will be 4 + 5 9 After that dear children how much Will you go? eight and one nine and also 7 3 10 8 18 Nine was cut. So what's left? Its digital sum is He just came. Did all the children understand? How did you remove it? a came. Now tell me the maximum value of a We have to take it so that this number gets deducted from three. So what is the maximum value of a you would take? If you take the value of a as nine, then the digital equivalent is nine. and this number will also be divided by nine and so a What will be the maximum value of? nine. To understand Did you come? All the children are doing it. very nice Yes. Come What is the question of CGL 2024 Pre? In? What is the sum of those possible values ​​of k? for which this seven digit number Are you divisible by three? Do you understand what the question is? Any number of possible values ​​of K So that the seven digit number gets divided by three. What to make of all those values? sum I have to tell you. Did you understand, children? If this number is divisible by three then K of all possible values ​​that are civilized Tell me the yoga. If this number is divisible by three then its digital sum is also divisible by three will be. We will extract its digital sum. digital What will come of it, dear children? Tell me. 3 + 6 9 and this means 2 5 7 and 7 14 2 5 7 7 14 5+ 5 + 2k this is it check it again 6 3 9 left two or or you can do it like this too dear children 6 3 9 5 + 7 12 also subtracted from three 5 + 7 12 What is left of three? Two left. 2 + And k + k 2k this is how digital sum comes in a way From. This reminder is coming when dividing by three Is. So if I take two common ones from here What will be left? 1 + That means dear children, give me 1 + this So it won't be enough with three. Only 1 + k such We have to take it so that it is three times the value of k. What can be taken? You can take two values ​​of K. 2 and a 3 cut Will go. You can take the value of K as five. Five And a 6 will be cut. You can take the value of k as eight. yes. 1 + 8 9 will also be divided by three. from eight You won't take a bigger one. If the value of K is 11 then you will take No. 1 + 11 12 is being cut like that. But 11 So it has become double digit, right? So these three values It is possible. What will be the sum of these? 2 5 7 8 15 is correct, right? Are? Must have understood? Let's move forward Let us go. Three's over. Now we come before you People at nine. The next type will be dear Children. Now onto the rule of nine. You have four numbers Have given. asked which number is greater than nine It is divisible. Tell me clearly which one The number is divisible by nine. so so It is not that you can multiply every number here by nine. Run away. What will you take out? Digital Sam. Correct Are you kids? What will you take out? Digital Sam. Tell. So if a number is divisible by nine If it happens then the sum of its digits i.e. Should digital sum also become nine or zero? Find the digital sum. nine 7 3 10 8 18 means this 4 + 2 6 is nine It will not cut. Here we will calculate 5 4 9 2 7 9 Its digital sum is three. Nine won't cut it. They take it out. 9 4 5 7 3 10 8 18 18 Meaning nine. It was cut by nine. So the answer to this What will come? D option. D option has come. All Had children. Let us tell you further. If this eight digit number is given to you. Eight The number of digits is 5 1 8 3p 47. These eight digits If the number is divisible by nine, then the number of p Tell me the maximum value. If this eight digit number is divisible by neither p nor What is the value of? If it is divisible by nine, then this What should be the digital sum of the number? nine. Take out the digital sum, dear children. 1 + 8 9 5 + 4 then see 7 3 10 8 18 Meaning removed. what's left of it Digital even? If P is left then what is the maximum value of p Can you take it? nine. So the answer to this question This is option D. Understood kids? Let me tell you this. If these seven digit numbers are 9 3a 5 We have 62 divisible by nine. This is a seven-digit The number is divisible by nine. So I asked a + What is the minimum value of b? give it here Digits are missing. a and b I have not asked for respect. What have you asked? of a + b Minimum value. Got it? a + b has asked. If it is divisible by nine, then the digital sum is also Nine should have come but nine got removed. 3 + 6 is 5 + 2 7 + a + b It will come dear children. These What happened to this number? This is the digital sum of this number. dear Children. You will say yes sir, absolutely right. So you have been asked for the minimum value of a + b. What have you asked? So tell me what should come in place of a + b Keep that this becomes digital even nine so two. 7 + 2 9 then the minimum value of a + b will be two. Yes, if in this question you ask for a + b Maximum Value asks for the maximum value so a What is the maximum value of + b? If we ask for the maximum value of a + b, this also So the question can be made for two marks, right brother? The sum can never exceed 18. a + b even if it becomes 9 is not greater than 18 Will come. So look, 7 2 9 is becoming digital sum. nine. See if the digital sum comes to nine or 18 or 27. It is the same thing because everyone's marks What is Yoga? So if I take a + b 2 Digital sum nine will be formed. So if you want to make 18 So what will come next? If the value of a + b is 11 If we take it, what will become of digital sum? 7 + 11 18 also means digital sum nine. then a + b What will be the maximum value of? To make 27, we will say 27 Sir, do 27. Is No? If you make 27 then what will you have to take a + b? If 20 and 20 a + b are possible then what is the maximum of a + b What will be the value? 11 Did you understand, children? Very Excellent. Come on kids, let's move ahead. Tell me do it. If this number gives you a great number Have given. is divisible by the smallest od Composite number. Now look at the number system. Went. This number is the smallest odd composite number is divisible by. Then what is the value of p? Then find the value of p. This number smallest odd composite number smallest is divisible by an odd composite number. So What are composite numbers? composite number Which have at least three factors. As That four six 8 but all these are even. what next Will you come? What will come to nine? nine. So Smallest Odd The composite number means nine. If If a child doesn't know, ask questions. Will he be able to? No. So indirectly This means that this number is less than nine It is divisible. So you are asked for the value of p. If this number is divisible by nine then Digital something should be no. So you can use its digital equivalent Will remove it easily. Will calculate digital sum. 3 + 6 9 and this 9 2 + 7 1 + 8 9 5 + 4 9 What's left dear children Here here this is left two and this is left three And this is the remaining p, if we add these then we get If you add 2 + 3 5 + p, it will become digital. how much should the sum become digital sum then you Tell me what value of p can you put on it? The value of 4 is 5 + 4 = 9. The value of p is 4. Option A. Tell me, did you understand or enjoyed it? Let me tell you this. Which is the smallest number among 7 84 89 656 should be added so that the resultant number is nine Are you divisible? What should be added to this This number should be divisible by nine. What does it mean This number is not yet divisible by nine. remained. What should I add to this that cut from nine Go. Isn't it? If this number is divided by nine If it is not happening then divide this number by nine. After doing this, some reminder or the other remains. And What is that same reminder? Its digital equivalent. So You can calculate its digital sum. What is digital Will you come? nine. What will come after that, my love? Children? 8 4 12 6 18 means nine. You We'll see 7 + 8 equals 15 and 6. The sum of the digits 21 21 and 5 21 and 5 26 is eight Its details have come as even number 8, right 7 8 15 5 20 6 If we add the digits of 26 again, we get eight. I can say this number divided by nine On doing this, a reminder comes at eight, if it is kept at nine If I divide by then what will be the remainder? Eight now What should I add to this so that eight is subtracted from nine. If you add one to it, it will become a digital sum. goes to nine and the number will be divisible by nine So what should I add to this number? need one Ok. Okay, everything is going well, right? Come Dear children. CHSL Pre 2023 This is a question of paper. do it. Are? Are? What will work? Yes. Mix will do brother. of three Read the divisibility rule. reading of nine Took. Now the mix will work. Come. What will be the largest number? 3 2a 7 8 b which is divisible by three but not by nine Not divisible. Who is the largest number C is of this format which is divided by three But don't cut it from nine. The question is going on fiercely. Okay kids? Yes sir. Find the largest number such that The number is divisible by three but not by nine. Don't be divided. It is not divisible by nine Meaning its digital sum should not be nine. It is divisible by three, which means Digital sum may come three or six but nine Should not come. To understand? Because nine If it goes or zero comes then the number is cut off from nine also. Will go. So one thing is that you solve it Do it. Secondly, you catch it from the option. We catch it from the option itself. We most A large number is needed. But what is the problem That two digits are missing here. A and B. These When will the number become large? When a large digit Should be kept. If the starting digits are larger then The number is large. So a big digit Should be. a must be a big digit. There are four here. There are six here. here instead of a It is nine. There are nine here. That means the biggest These are the ones. Isn't it? This one is the biggest Is. 329 787 Because there are four sixes here. So This number is the largest. checking this Are. Is it cutting through three? So its Find the digital sum. The digital sum will be 9 2 + 7 9 7 3 10 8 3 8 11 7 18 18 means digital sum nine. So this means the digital sum of this number Nine is coming. So this number is subtracted from nine. While we are looking for a number that is larger then It should be the largest but not divisible by nine. Needed So this was removed. Then it won't happen Then we will check this. checking this Are. Digital sum of 9 2 7 9 3 8 11 4 15 15 The digital sum of 15 is 1 5 6, that is, these six The digital sum is being deducted from three but This is the biggest number after nine. this that The largest number found is these four numbers I am not able to cut it with nine but they are able to cut it with three. I will not check. If the question has the most If a large number is given, then the largest number is given first. I will check it myself. It's not that I'm younger than the Let me start checking. Isn't it? any good way pain? Let's move ahead. Tell me dear children. Live here. SSC GD question In the examination of 26. Isn't it? great question Is. Who will do it? Which of the following numbers is not So it is neither divisible by three nor by four. So Let's see this. This number is divisible by four. Not there. Isn't it 41? The last 41 that are coming and 9 4 1 5 are also divisible by three Not there. I mean, what is this? Answer. So this Look, the GD people ask this, my love Children. Isn't it? These numbers are the last two 41 Is. It won't cut it with four. its its you If you calculate the digital sum, the result is five, that is That's three options. Let's move ahead Dear children. It has reached this point. Now I will come now, I have explained to you three. Divisibility rule and nine. Now what is Questions will come which will have meaning to solve More than two will force you to apply divisibility rules. Will fall. two or three times Divisibility rules will have to be imposed. Come Dear children, we will look at each one of you. First of all, you will come across six Question on divisibility rule. not six taught. What is six? 2 * 3 so any A number is divisible by six only if it The number is divisible by two and by three It should also be divided. That's all there is to know. Come Please go. NTPC 12th Level CBT One This is the latest question of 2025. Which one The number is completely divisible by six? Who C number from ch? Completely Dil Ch Se Katne Ka means Chha means 2 3 6 Chha will cut the same number which is divisible by two and also by three Divide the first number you will see in the last One is coming, it will definitely be divided by number two. No, this too will be divisible by two, this too will be divisible by two. This too will be divided by two, it will be divided by three. Stuck in the choice, what to watch now? If the number should also be subtracted from three then Let's see if it cuts through number three. 6 3 9 7 2 five and one The digital sum of this number is coming. That means that This number is divisible by three. Last If the digit of is even then it is divisible by two. Has been. This means this number is divisible by six. It will happen. What is its option number? Correct B. When B finds the correct option, check further. There is no need to do it. Okay, right? Okay kids? Option B is the answer. Correct Is? Let's move ahead. The next question is Tell me about NTPC. If this seven digit number is divided by six It is divisible. With whom? is divisible by six. So tell me the minimum value of a. Brother, if this If the number is divisible by six then it is also divisible by two It should be cut and also by three. If this number If it is divided by two then the last digit It will be even. Eight. That is, this number is less than two It is divisible. Now from whom should this number be deducted? Needed? It should be cut into three also. just me Here the value of a has to be taken as follows The number should be crossed out by three. Come on, because from two So it is being cut. If it is cut by three Its digital sum is also divided by three. Needed So nine six 3 9 then five and three Eight and eight is 16, meaning 7 + a, what is this? Digital Sam. What do you want to take? of a Minimum value. The minimum value of a is to be taken So that it gets cut by three. With whom? Three From. So you 7 and one is eight 7 2 9 so a What is the minimum value you will take? So two If you take it, nine will be deducted, dear children. Three From. Let me tell you this, dear brother. do it. If this number is divisible by six. With whom? ch From. So the sum of all possible values ​​of m Tell. If this number is divisible by six then For all possible values ​​of m Tell me yoga. Brother, if this number is less than six It is divisible. Six means 2 * 3 = 6. If this number is divisible by six then two It should be divisible by 1 and also by 3 There should be a divide. If this number is divided by two If there is division, think about the last digit. What is? So what will be the last digit? Even. What should be the value of m? to be even Needed So this is the compulsion of this question that m What will be the value of? That is, the value of m is either It will be 0 or two or four or six or else m may have no value at all Can. Now this number is less than three. Needed It should be cut into three also. So its The digital sum should be divisible by three. So You will calculate its digital sum. Digital Sum Take it out. 6 3 9 7 2 So what's left? Eight. Eight escapes And m + 0 + m means 8 + 8 + 2m Digital Sam came. The value of m is to be taken such that This digital sum should be cut off by three. If I If I take the value 0 then 8 + 0 is not 8 by three It will be cut. I will take the value of m as 2. 2 * 2 = 4 8 12 It will be cut by three. I will take the value of m as four. 4 2 6 8 4 * 2 = 8 8 16 will not be divided by three. m I will take the value of six. 6 * 2 = 12 8 20 no It will be cut by three. If I take the value of m as eight, then 8 * 2 = 16 8 24 will be subtracted from three. That means that These are the only two possible values. two and eight Right, we can keep only two and eight. Then m What will be the sum of two equal values? 2 + 8 10 Isn't it a good question? 20 20 I am telling you brother, 10 will come. half 50% Even the children are so small that they can be explained. Despite this, I was able to give the correct answer. We will move ahead. So Who did this happen to? At six. I give you every single I will explain the pattern. Now I will get it done on 24th. 24 On the divisibility rule of. I have taught 24 What? No. You can write 24 as 8 * 3 A number is divisible by 24 only if it The number is divisible by both eight and three Be divided. That's it, the rule of 24. Come Dear children. Come on, tell me. If this seven digit number is divisible by 24 If it is divisible then it is asked what is the maximum of a + b What is respect? Brothers A and B are missing two digits. first thing So here we get different values ​​of A and B. Don't have to take it out. You won't take it out, right? What Want to remove it? a + b then if this number is greater than 24 If it is being divided then it should be cut by eight also. Eight will give the value of b. He -- me Don't take it out. If this number is divided by 24 If it is happening then it will be divisible by three also. And If it is divided by three then its digital sum is What should come? The one that cuts through three. So You will calculate its digital sum. Digital Sum What will come, dear children? 4 4 12 7 19 19 7 19 7 26 means 8 + a + b this is what we get of the number Digital Sam. Now you tell me what is the place of a + b Should we use the maximum value instead of a + b? So that this number is divided by digital sum three. Go. So instead of a + b, by maximum option Just look at it. If I keep 16 then 8 + 16 is 24 And the digital sum of 24 becomes 2 + 4 6 i.e. That will be cut by three. Then the maximum of a + b Have you got respect? 16 has already arrived. Tell me someone Are you in pain? Did you understand, my brother? So There is a need to apply the digitization rule of eight. I did not even need it. How did it get resolved? from three It's settled. Is it okay kids? Let's move forward Are. next question. Next will come dear children On the divisibility rule of 36. taught 36 What? No. 36 is four names. if anyone If the number is divisible by 36 then the number Any number that is divisible by four is also 36. divisible by only if it is both four and nine It is exactly divided from this. Ok Children? Let us tell you what the answer is. This is a good question. This is a nine digit number. Divisible by 36 Is. What is the value of x / y - y / x? for the smallest possible value of y? Question This is tell me if this number is nine digits If it is divisible by 36, then x / What is the value of y - y / x? and x / y - y / x will only occur if both x and y have values You will find out. for the smallest possible What are the values ​​of y and y you need to take? Smallest value. Multiple values ​​of y Might be possible. I have to take the smallest one among them. Given that x and y are natural numbers. x and y is a natural number. Natural number means x and Both y values ​​are greater than zero. This only The thing is. Isn't it so, children? Now tell me if If this number is divisible by 36 then its This means that this number must also be divisible by four. Should and from nine too. is divisible by four So the last two digits should be subtracted from four. What are the last two digits? y four. Should be cut into four. So tell me I am replacing y. What can I keep? 0 will be cut off by 4. But y cannot be replaced by 0 because 0 is a If y is a natural number then you can replace y with zero. Can't. If you keep 14 one, 14 will not be cut. What will you keep with four then? Two. If you keep two This will become the number 24 and 24 is divided by four. Is. So you need to take two values ​​of y. Will have to. Can't take 0. Did you understand the matter? In? So this is how you have to think. So after solving here, I got this value of y. Took it out with a bang. What has come? of y Give it your respect. The value of y is two. But The question remains unresolved because what we Want to remove it? The value of x. How will the value of x be found? Brother? Because this number is subtracted from 36. So this number must also be divisible by nine. It will be divided by nine. This means that this number What will be the digital sum of this? Nine. So now You will find the digital sum of this number. I put the value of y as two, so 7 + 2 9 4 3 7 2 9 and 8 + 1 is left over and this is x and the remainder is Four means the digital sum of this number is Dear friends, x + 9 is the sum of this number. digital sum and digital sum should become nine if If the digital sum is nine then what is the value of x must have been five because 5 + 4 is 9 of x Let's say five is the value of y, and this is where the question ends. It happens. Yes kids, just keep the value. x The value of y is 5 and the value of y is 2 so 5/2 - 2 / 5 Bhaiya, it will come down 2 * 5 = 10 and it will come up 25 - 2 * 2 = 4 21 / 21 /10 Answer. 21/10 means 2 correct 1 / Correct. How did you like it, my brother? Are? Is everyone's B coming? Very nice sir. Well, that's it, dear friends. Now 36 The one will now appear before you here. 45. We will ask one question each of 45 and 18. I have found the divisibility rule for each number. I asked a question on this. nothing left. Ok No? Come on, tell me this. This question right now Latest NTPC 12th Level Papers I have come. Isn't it? And of course SSC too These Railways and SSC copy questions among themselves. live. We And we are taking care of both the children. ok sir. do it. This five digit number is divisible by 45. Is. where a and b are both positive integers Are. Both a and b are positive. have asked What is the value of a + b? Okay, right? Now Hear No rule of 45 was taught. So What will Govind ji do then? Meaning of 45 9 * 5 is nine and five together is coprime. Then a number is less than 45 only It will be divided when it is divided by five and becomes nine. Cut from this also. That's it. If this number is greater than five If it is being cut then the last digit is b then The last digit b will be either 0 or It will be five. But b cannot take the value 0. Since both a and b are not 0, the value of b is What is the value of b? It's five, right? So one of our problems has been averted, how can we say that B's The value here is five. In place of b, you put five. Now what do we have to calculate, how will a come? If this number is divisible by nine, then quietly What should come digital sum nine digital sum take out take out five more here 5 10 3 13 13 7 Sum of the digits of 20 Sum of the digits of 20 2 + So the digital times of this number is 2 + A and What should be the digital equivalent? nine. Then A will respect 7 2 + 7 9 so brother the value of A is seven and that of B is Value five. So A + B comes to 12, isn't it good? Question? Option number D. Come. Let's tell you this Dear children. 8 97 65 a4b How many letters of a and b are there in the number Are pairs possible? If this number is divisible by 18 Tell me if it is divisible. If this number is divisible by 18. Hey Wankhede ji, tell me this number Then how many pairs of a and b are possible? What The Divisibility Rule of 18 was taught to you. Is? No. But it taught you so much that 18 means 9 * 2, any number is 18 only then It will be divided when it is divided by nine and by two. Also cut. And if a number is divisible by two If yes then what should be the last digit? Even. What will be the last digit? Even. That means whatever will be the value of B dear Guys, that would be even. then B is either zero or two or four or six or more B will have no value at all. Is it okay? Children? nine. If this number is divisible by nine Then the sum of its digits i.e. digital sum should also be cut from nine. So what will you take out? Digital Sam. So it became nine. 5 + 4 becomes 9 So the sum of the digits of 7 and six is ​​13 13 and eight is 21 The sum of the digits of 21 is three i.e. 3 + a + b Brother, two digits are left out of seven 7 6 13 8 21 Sum of digits three one digit a left over one b So 3 + a + b is your digital sum and digital sum should become nine digital sum nine Should be made. Isn't that it, kids? now you see Because here A and B are asked how many pairs Will it be made? Let's see one by one. If the value of B is taken to be 0, then what is the value of A? Will I take it? What value will have to be taken for A? Six Because 6 and three is nine. Digital sum will remain nine. Once a pair is formed, I cannot take anything else. If the value of B is two. So tell me about A What will be the value? Then three and two make five. of A I will have to assume four. 5 4 9 if the value of b I'll take four. Four so what will have to be taken? Then b takes four. Three became four. 3 4 7 So a will have to take two. 7 2 9 if b of Let the value of 6b be 6 then 3 + 6 is 9 Then what will be the value of a? 0 9 + 0 9 This is where the problem arises and the reason for this Children will make mistakes. This is what needs to be explained In this question. If you find the value of b If you take six here, then 3 + 6 You can take the value of a. 9 + 0 digital even 9 but you can also take the value of a as nine Because 3 + 6 equals 9 and 9 + 9 equals 18 in digital form. Sum again brother 3 + 6 9 + 9 18 18 digital sum again so here the value of a in this case It could be zero or it could be nine. Is. Both values ​​of a are possible here. Tell Did you understand or not? The value of A is 0 It can be one or even nine. Is it okay? Children? Maximum children know this thing Will not catch. He will understand that 3 + 6 9 a 0 do. But a could also be 9. 3 6 The sum of the digits of 9 18 is also nine digitally. Even. Let's move ahead. Now in front of you The value of b will come if the value of b is eight then this Done 3 + 8 will add seven to 11. 11 7 18 means the sum of the digits 11 7 18 18 is nine. Digital sum 9 18 27 all the same thing. So you Tell me how many pairs of A and B are formed here? These These are four, but two pairs with six. Will be made. 0 6 and 9 6 then the total of A and B How many pairs will be made? These six pairs. what is the answer Is? Are? Tell me dear children. Did you understand? You You will say yes sir. It ends with this It happens. Let's move on now, your Front. The number on which most questions come There is his divisibility rule in your paper Tell me, what do you get the most questions about? 72 Pay. Most questions come in mixed. On the divisibility rule of 72. most Yes children. Now tell me I did not teach you the divisibility rule of 72. I can write 72 like this. 8 * 9 72 8 * 9 = 72 eight and nine together is coprime. You also know the rule of eight. You know about nine also. If a number is eight It is also divisible by 10 and also divisible by 9 If it happens then the number will be divisible by 72 also. Understood? You will say yes sir. This is what you Have to apply it. Come dear children, here is your Front. do it. Brother, you haven't got 50 likes yet. As such How will things work? All the children who are studying are 50 at a stretch. There should be likes. Like it all, only then you will enjoy reading. Will come. Isn't it? Like it three times, son. of the house You can like it even after snatching the phone. If this nine digit number is which nine digits? This is the number of points children get from 72 If it is divisible then what is the value of 6x + 7y? If you want to solve the question, then take out x also. You will have to remove both. that is No? If this number is divisible by 72 then This means this number will also be deducted from eight and nine From also. If this number crosses eight then The last three digits should be subtracted from eight. The last three digits are 7 8 y The last three digits should be subtracted from eight. So what should be replaced by y to cut it by eight? Go. What should be taken in place of y? So you see 8 * 9 is like 72 is 78 right? 8 * 9 72 What's Left Will you go? six. Now this is y so what should come in place of y will have to take? 8 * 8 = 64, 64 will be the multiplication table Or not from eight? 8 * 8 = 64 i.e. y There can only be one value here, four. y The value of came to four. 8 * 9 = 72 6 left. 6y then 8 * 8 = 64 will have to be kept. Isn't it? So y 4 Now I took out y with a jerk. Four. Now whose compulsion is it for me? Then Whose compulsion? to remove x. What to remove? x x how Will you come brother? If this number is divisible by 72 If it is, then it should be deducted from nine also. Now what Will you apply it? Divisibility rule of nine cut by nine If it is there then digital sum should be nine. digital Please apply the same here dear children. Nine cuts Went. Ch 3 nine cut off. then seven and 8 15 3 18 This is cut. So how much is left? eight and four eight and four equals 12, that's 3 + this is your digital is even and should become digital even nine. digital If your nine becomes friends then the value of x What will come? will remain Ch. Will it remain six or not? If the value of x is 6 then take this value Will keep it here. The value of x is 6 then the value of y is 6 How much? 4 * 7 so 36 + 28 36 + 28 64 and the under root of 64 is eight. So this The answer to the question came out to be eight. Tell me if there's any problem No, right? Ok? Let's move ahead. This will tell Dear brother. If this 10 digit number is divided into 10 digit The number 5 4 72 68 79 y6 is divisible by 72 Is. Then for the minimum value of y, the value of y What is the minimum value of 5x - 3y? Will it happen? What do you need to figure out in this question? My brother? In this question you have to find the sum of 5x - 3y. Have to take it out. But when? When the value of y is minimum yes. Now tell me if this number is divisible by 72 is divisible by both eight and nine It will be cut. If it is deducted from eight then the last three digits Should it be cut by eight or not? The last three The digit is 9y And the last three digits should be subtracted from eight. Now tell me what you want to replace y with y. Minimum value is the minimum value of y to be taken. So you tell me You tell me dear children what is the place of y What should be kept at least so that it gets cut by eight Tell me what to keep What should be put in place of y so that it is cut by eight It's like 9y 6 what is 9y So look at this, it's greater than 900. So 900. If it doesn't cut into eight, you can write it like this be 800 + 1y 800 + 1/6 because 800 + 100 is 900 Can't write? breaking you like this Needed This number 800 will definitely be divided by eight. That is, only this should be deducted from eight that No? So tell me what should I put in place of y? 106 It will not cut. 116 will not cut. 29 * 4 = Even 116, 126 will not cut it. So 14 * 9 = 126 You will have to put three in place of y. If instead of y If you keep three then it will become 136. from 136 Deducted 17 * 8 = 136 17 * 8 = 136 So what will be the minimum value of y? Three. Is No? Good. So keeping zero here does not cut it. remained. From 1068. Keeping one is not enough. Two It is not cutting it by keeping it. Cutting off on keeping three Is. So the minimum value of y is three. Let us go The fight with Y is over. What do we have to get out now? Is? x The value of y has already come to three. What Do you want to take it out, dear friends? Now What is the value of x, tell me children? What will happen? x is here. How will the value of x be found? if these If the number is subtracted from 72 then this same number is nine. It should also be divided by this. If this number is divisible by nine If it is dividing then what is its digital equivalent? will form? Its digital sum will be created. Will take it out. 3 6 9 and this 9 2 + 7 9 5 + 4 9 The sum of the digits 7 and 6 is 13 Four 4 + x will become digital sum and digital Even should become nine. If Digital Sum Nine If this happens then what will be the value of x? The value of five x will be five. So 4 + 5 of x The value five came in and the value of y came out. These Let's keep it here. The value of x is 5 * 5 = 25 y The value of 3 * 3 = 9 so 25 - 9 is 16 Is. Tell me option B. Did you understand or not? Did you enjoy it? Is it okay my brother? Let go Let's move ahead dear students. Now we Will ask the last question on 72. Are? Enjoying it Don't the children have it? do it. This is of 10 marks Number: This is a 10 digit number. 72 From It is divisible. This 10 digit number is divisible by 72. It is divisible. Then what is the value of 3x + y? What is the value of 3x + y? for the Possible greatest value of y? If y Value is the best of the greatest. Tell. If I say that till now all the questions I have asked The best and deepest question among them is this Is. Isn't it kids? If this number is divisible by 72 then 3x + What will be the value of y? If you The greatest possible value of y You accept it. Brother 3x + y will come only when you multiply x We will also find the value of and the value of y Will take it out. Without x y it will not happen. Let's say this number is divisible by 72. This number is also divided by eight. Should it be cut or not? If this number is divided by eight If it is being cut then its last three digits are eight Will be cut from. What are the last three digits? 7x 7x2 Now tell me what number should be put in place of x Should it be such that it gets cut by eight? what number should be put in place of x my brother That it should be cut by eight. tell me where x is What should be put in place of x so that it gets subtracted from eight? Look, this is bigger than 700. x is a digit. 0 It can be anything from 1 to 0, 1 to nine. Is. This number is greater than 700. Not 700 Cuts by eight. Use your brain a little. You You can write it like this. 600 + 1x2 ok? 600 + 100 is 700, right? Can write. You Think for yourself that this is divided by 68 75 times. 600 is deducted from eight. That means only this one You have to take such a number that it is divisible by eight. So tell me what should I take? If I replace x with 0, I get 102 eight. It will not cut through. Then we'll replace x with one. 112 will be cut off by eight. Then 122 will not be cut. There are 12. 122 from eight It will not cut. 112 will be deducted. 122 will not cut. No 132 It will be cut. Are you children, dear children? Even 142 won't cut it. What will be cut? 152 five. Actually you should understand that like this forest And this x and this two should cut off this eight. These Who should cut the number? Don't change me one Isn't it, I have to change two. I will tell you a trick I am here, dear children. Don't change me one Isn't it, I have to change two. just the middle digit It has to be taken in such a way that it keeps getting cut from eight. So I Tell me if I add 40 to this. 40 So this Look at the 1x2 also being cut by eight. 40 also from eight It is being cut. What is the benefit of adding 40? That the last digit will not change. But this The number will always be subtracted from eight, No? So if this is 112 divided by eight. Next, 40 plus 152 will be subtracted from 8. and next 40 plus 1192 will be divided by eight. That is, x What could be the value of? nine. Even if you divide 112 by eight, even 152 It will be cut, 192 will also be cut. So here x Three values ​​are coming. Our view is this that the maximum value of y should occur. And Where is y coming from? Here. So we have that case Find where y is maximum. I enjoyed it No? Now let's say we have three values ​​of x. I took it out and kept it aside. 1 5 and 9 If this number is divisible by 72 then this number If it is seven then it should be cut from nine also. nine If it is cut from then its digital sum should be nine. Please find the digital sum of this number. By using your brain. Will digital equality come, dear? Children? Tell. 9 7 3 10 8 18 means 9 these 9 7 2 9 then remainder 5 + x + then of this number The digital sum is 5 + x + y and the product of this number is Must be digitally equal. Nine because this number is subtracted from 72. This is a question asked in the paper. What will come? Details should be nine. Now we have to take Greatest value of y here. good if I take the value of x to be one. What should I take? So how much will I have to take? five and a 6 y will have to take. 3 6 3 9 brother three values ​​of x right here 1 5 and 9 if I take the value of x I'll take five. What should I take? The value of x If I take five, what about 5 5 10 10 Couples? 8 10 8 18 10 + 8 18 and 18 means 9 So what will come to y? Eight. If I set the value of x to nine I take it. What should I take? nine. So 9 5 14 I'll add four to make 18. 18 18 means digital Even. So here these three values ​​of y will be formed. How many cases will be made? Three cases of y will be formed. But you get that where what is the value of y? So where is the maximum value of y found? Eight. That means you neither have to take this nor You have to take this. What do you want to take? Then x What will be the value of? five and the value of y is eight. y The value of eight. So the values ​​of x and y are given. These Put the value here now. The value of x is five Will keep it. 5 * 3 = 8 in place of y. 15+ 8 means its answer will be 23. Tell What kind of question is this? Are? Is it or not my brother? I had a lot of fun doing it. So it is not necessary that every question, dear friends The problem will be solved immediately. Any question 5 seconds Some get solved in 10 seconds, some in Someone happens in 1 minute, someone happens in 1.5 minutes Not there. Are you understanding my brother? Of everything There are different statuses. Somebody earns ₹300 a day earns, some earn 3 lakhs, some 30 Lakhs, some 300 crores. Are? Ok? So you have to read every type. every Stop weighing the question on a single scale. Isn't it? The importance of each question is different. Correct Yes sir. Well, it had come to this. Let's move ahead. So dear brother is it done. I 2 3 5 7 these 11 9 all Got the questions asked. Got it mixed as well. Now And let's move forward, dear children. Mix We have a lot of questions. Your Will come forward. Now Which one is it? Yes, on 88. Okay kids? Come. This is a question from CGL 2023 Pre paper. Are Tell me children. If this nine digit number is 88 This nine digit number is divided by 88. x and y are natural numbers. So I asked about y Value of x² + y² for smallest value What will happen? This is a white number from 88 It is divisible. So I asked you what is x² + y² will be? But the condition is that you should get the most Have to take smaller value. Smallest Value I have to take it. Isn't it kids? And the condition is also that Both x and y are natural numbers. That is, x and y are both greater than zero. Did you understand? Children? Now I have told you the rule of 88. I have not taught. Didn't you teach me? But you Do you know that 88 means 8 * 11, so if someone The number is divisible by both eight and 11 If it is divided by 88 then it will also be divided by 88. Let's say this number is divisible by eight. So what are its last three digits? 2 / 2 / 8 The last three digits of the number Is. 2 / 8 ok? If this number is divided by 88 then it becomes eight. It will also be cut from. So the last three digits are from eight. Should be cut. The last three digits. so me Tell me what value of y should be taken so that it is cut by eight Should I go? What value should be taken for y? If you replace y with zero, you get 208 8 * 2 ni 16 8 * 6 = 48 will be deducted. what is the value of y Went? 0 is the smallest zero. But you are zero Can't take because what is y? then until the value 0 is not taken. By keeping y equal to 0 It is being cut by 208. at y ≥ 0 is not possible Is. Because y 0 is not a natural number. Zero is a whole number. So y you not zero Can take it. Then what will you take here? Adding four gives 248 if you replace y with four. 248 will be divided by eight 8 * 3 = 24 8 * 1 = then instead of y you will have to take then four Did you understand, you can do it like this too 2y8 You can write it like this 200 + y 8, this is divided by eight. If it is cut, then we will have to put four in place of y. Because 48 will be subtracted from eight, so y The value came from here to four, now what do you I want to find the value of x. Tell me how will x come out. My brother, the value of y has already reached four. Now how will x come? Brother? listen if this number If it is being cut by 88 then it will be cut by 11 also. So 11 Apply the rule of. And what is the rule of 11? Odd And you will calculate the digits in even places. Even. Then what is the sum of the digits at the odd places? Will you come? 9 + x + 5 9 5 14 2 16 16 8 24 9 5 14 2 16 8 24 + x 24 + x ok kids and You will find the sum of the digit at the odd place i.e. that 7 4 11 11 6 17 and 4 17 4 21 this will come, their difference either Should it become zero or a multiple of 11? Can their difference be zero? We don't see this happening because 21 is greater than 24 which is the smallest number among the larger If you don't get zero after subtraction then what will you become? Needed This difference should be 11. If it is 11 So tell me when will 11 come? When will 11 come? When will 11 come? When 21 out of 32 Should it be reduced, that is, how much should it become? This value should become 24 + x. 32 32 - 21 = 11 then the value of x will have to be taken as 8 24 + 8 Anyone can solve it, so x = 8 and y = 1. Four comes, x is 8 and y is 4, so we will keep 8 here. squared 64 and y 4 squared of four so 64 + 16 80 80 is the answer It's easy, isn't it? okay brother. Let me understand you talk? We will move ahead. This will do it. next The video quality is great today. The children are having fun. What did he give ₹40 for? Drink the tea. To drink tea. I don't drink tea at all. I only drink water. It's already 11:00. At least 3 hours now We will read more. It will last until 2:00 Yes. Are? Who wants to study until 4:00 in the morning? Vote. Wants to study till 4:00 in the morning. Comment everyone. Let me tell you. If the nine digit number is divisible by 99 Is. Hem Wankhede ji, great question. Now it has come Fun because now my brain is hanging Is. If this nine digit number is divisible by 99 then what is the value of a + b + c? A B C I have not asked, I have asked A + B + Bhaiya 99 You don't teach the rules, you ask questions. This way How will it work brother, brother, 99 is 9 * 11 9 11 is coprime. If a number is nine It is also cut by 11 and then by 99 Will also be cut. Let go If this number is divisible by nine then digital It should become equal. nine. Let's go digital Are. nine nine nine what's left? six and 5 11 6 5 11 Brother. Hey, calculate the digits 6 + 5 11 11 Add two and these three digits are left. a b and So 2 + a + b + c is your digital sum and Digital Sam should be created. nine. So brother, the value of a + b + c is like this We have to take it so that it becomes digital sum nine. The number should be cut off from nine. So take it from the option Are. If you take a + b + c 16 16 two It will be cut by nine. Even if you take seven, it will be cut. 26 two 28 if you took a + b + c 16 26 So 26 and two will not divide 28 by nine, so 26 will It won't happen. If you take a + b + c 25 25 two 27 will also be divided by nine. So that means The question has not arisen from the option whether or not Children? Then you will have to work hard further. Is it okay kids? Listen. If this number is less than 99, it means This number will also be divided by 11. So the rule of 11 You apply it first. 6 and 9 15 15 5 20 20 9 and 9 38 38 came even even digit of odd place The sum of the digits of the place is 0 + a + b + c then 0 + a + b + c comes a + b + so this difference Either it should become zero or it should become difference This difference should be a multiple of 11 or Will the child become zero or 11? Now if I take 16 away, 16 is 38 - 16. Will come. 22 is a multiple of 11. That is, the number 11 From It is divisible. If a + b + c is taken to be 16 So 16 + 2 18 means digital even nine. This number is from nine It is also being cut. So taking a + b + c 16 gives The number is also being cut off by 11 and simultaneously nine It is also being cut off. That means it is a cut from 99%. Will go. So what will be the answer? Sir a + b + c 16 If you take a + b + c = 7 The number 2 + 7 9 will be divided by nine but a + If b + c is divided by seven, the difference will be 38 7 31 from 11 so it's possible if you have a + b + c 25 then 38 - 25 13 number ever It will not be cut by 11. So it cuts off from 11 only then What will you get when you take a + b + c? 16 Got it? That's a good question. Let's move on Are. Ok. Ok. Next. Now we will do divisibility Miscellaneous Questions of Rule. That means this The question is. There is no fixed type. Is No? There are many questions from previous year. In. I will get something done for you. it Tell me. This is a UPSC CSET question. The CSET question has come brother. See Sir please read some other topic also Bhai Sahab Do not teach what you will teach I will teach my son now. I will teach you in Indonesia, brother. Damn you who are teaching silently. Read that. There should be no sound from the light at all. Ok? A B C D F both three digit numbers Is in this type. A B C D E F Different There are digits. No one is zero. non zero There are digits. A B C R Distinct Non Zero Digit. such that A B C + DEF = 1 1 No? What have you given? Both A B C and DEF What is the sum of the numbers? 1111 then to you The question is, what is the value of a + b + c + d + e + f? What is? That is, both of these numbers You have been asked to add the digits. have children a b c df what is this? a b c df both three are 1-digit numbers and where all the digits are What are they? They are different. Isn't it kids? And no one else is zero. look at it anyway UPSC has a different method of solving the questions. But if you think about this question then a + b + What is c + d + e + f? Sum of digits and Sum of digits means digital sum. if you Apply digital sum here so a + b + c d + e + f and digital sum becoming equal to 1 2 3 4 So the answer will be the one whose digital sum will be 4 3 + 0 3 2 + 8 10 means one 3 + 1 The four digital sum can be 2 + 1 This will not happen, there is only one answer which is digital. Becoming even four could be the correct thing. End Did you understand any problem? of a + b + c + d + f What was Digital Sum supposed to become? And that one The digital sum of the option becomes four. If The sum of the digits is 31. Sum of digits of 31 That means digital sum four. End. Come on sir. These Tell me. Are? Three digit numbers A, B, C, CAB and BCA Their sum dash dash dash is divisible by Not there? The Sum of Three Digit Numbers a b cab b and b ca is not divisible by batao These are three digit numbers. The sum of their digits Not divisible by what? There are four options. a + b + c 37 31 and three. Correct? Tell. Look, you can answer this question as per your wish. Take any value of ab bc. Like you can calculate the value of ABC Take 148. Take any value you want You can do it. But I want to explain to you Deep concept that more questions can be raised on it Can. Isn't it? Like these three numbers The sum of the digits of is not divisible by? There are four options. Okay, let's say three The number of points is written in front of you. For example, 8 7 3 is three. seven is the tens digit and eight is the hundreds digit Number of place. Units digit, Tens digit and 100 place digit. So how will you write this? 3 * 1 in 3 = one in 1 multiplied by seven in 10 multiplied by 100 and multiplied by eight. Then it becomes Isn't it 8 * 100 then it will become 800 + 70 + 3 870 Isn't that the case? So same logic here. Must be applied. a b c means a * b * c is not. This is not algebra. Number There is a system. a b c a three digit number Is. c unit digit, b 10 place digit, a 100 place digit. This means a b c 100a + 10b + c a means 100a + 10b + c like this What's up dear kids, cab to cabb What does 100c + multiplied by 100 mean in c 10+ b these kids what is the meaning of bca bca I am explaining to you in detail what happened. In bc means 100b + 10c + a and we have to What to do with the three numbers? Even. What is the sum of these three numbers? Is it divisible? When I sum up this mind I was the thing to do. So tell me how much Will the bar come? 100a Did I write it wrong here? This is 10a, right? 100a + 10a + a means 111a Then you look at b and look at 10b + b 11b 100b 111b c will also come c + 100c + 10c 111c i.e. all If it comes 111 times then the result will be 111A + 111B + 111 You can take 111 common. I will add everyone 111a + 111b + 111 There is a very famous number that you should know. Write down 111, it is 37 * 3 = 100 37 * 3 = 111 I will also teach now 37 * 3 = 111 a + b + c understand what I mean i.e. The sum of the digits of these three numbers is 37 37 is also coming in all the numbers three is also coming and a + b + c also so this number It will be divided by 37 and by three also a + b + c but is not divisible by 31. Option Number Got it? A is not an option. What is? C option is the answer to this question. This number Which will not be divisible by 31. All three of them Because the sum is also deducted from 37. from 37 is also coming. It is also being cut by three. and a+ is also intersecting with b + c. It was a good question No? You will say, Sir, it is very good. fun Came. The heart became a garden. of this Dear friends, this type ends Is. Now you will do the next Type. Next type: Dear children, special Numbers. Isn't it? Are you enjoying it? Special Numbers. Look, there are some numbers like this. Whom you have to keep close to your heart. in But questions come. Big interesting numbers There are. Interesting. Isn't it kids? Let go Look at the three numbers 7, 11 and 13, all three are prime numbers. When humans play with them He was doing this, so he saw that if these three were multiplied It should be done. What should be done with all three? 7 11 13 If all three are multiplied then 7 * 11 * 13 What will come? 1001 7 * 13 7 * 11 * 13 equals 1001. 7 * 11 * 13 = 100 Do you understand what I mean? These 1001 are very It is a famous number, it is divided by seven as well as 11. Also, if any three digit number of 1001 The concept of multiplying the number by 1001 Understand the concept, if any three of 1001 Multiplication of digit number like 1001 I multiplied 800 by 52, tell me, tell me the multiplication. What will come of doing this? Multiplying 1001 by 852 means If you write 1001 like this, what will you get if you write 1000 + 1 On multiplying? 852000 + 852 means what will be the result of multiplying Will you come? 85285 So we saw that if any three of 1001 The number of digits should be multiplied. For example, I took 85 So a six digit number comes and these six Number of digits corresponding three digit number It is formed by repetition of twice. That means that The first three digits are the same as the last three. It is a digit. Did you understand, dear children? Any pain? If any three digit of 1001 If the number is multiplied then that three digit A six-digit number with two repetitions of the number The number will come. Did you understand? Another one Let us take an example. Like 759. If If 759 is multiplied by 1001, we get 75975 That means a six digit number will come dear children in which the first three digits and the last The three digits will be same. Isn't it? These three The number of digits will be repeated twice. 759 75 Got it? So dear children, if I did 1001 in the same way. Multiply any three digit number. Suppose I have a three digit number AB of the form 101 I multiply in C. so tell me in a b c What will come after multiplying? Multiplication of 1001 by any three digit number do it. ABC is a three digit number. So that means A B C is repeated twice. Will go. A B C A B C A B C that No dear children? Did you understand? You You will say, Sir, absolutely correct. It's okay. Now I reverse this thing I write. What do I write? By doing it upside down. Listen carefully. If a six-digit If a six digit number is divided by three It is made up of repetition of three digits. if anyone Six digit number twice three digit Made from repetition. like ABC ABC then its This means ABC * 100 ABC * 1001 will come and ABC * 1001 Meaning 7 * 11 * 1001 means 7 * 11 * 13 This means A B C A B C is a six digit sequence. There is a number. Why is special special? Because these three digits are repeated twice. It is made by repetition. So this is A B C A B C will be divisible by A B C and also by seven It will be divisible by 11 and all these. will be. Dear children, I think this is Did you understand? Did you understand it or not? This might seem like a very minor thing to you. But the examiner asks questions on this. Come What are the numbers in CGL 2022 Pre? 11 is divisible by 13 and seven and is divisible by four Gave options. However, here we are talking about 11, 13, 7 You can apply the rule of. But you tell me If we see which number from 11, 13, 7 Is it divisible? So how many points are all the options? Who are you? Six digits. If a number is 7 11 If it is subtracted from 13 then 7 11 13 are If it is coprime then the number will also be divisible by 1001. If any number is divisible by 11 even by seven also and also from 13 so 7 * 11 * 13 is also from 1001 It will be cut. And if any number is divisible by 1001 is six digits, so the first three digits The last three digits will be the same. i.e That number will be A B C A B C A B C A Which option is BC? 269 ​​259 This number will be cut off by 7 11 13. Did you understand, children? No problem. Let's ask the next question. Do. A chocolate manufacturing company sells chocolate every hour to ABC Produces chocolate. Every hour A B C is making chocolate. ABC is a three Digit positive number. A B C three digit There is a number. In How Many Hours It Will Produce A B C AB C Chocolate. AB C How many hours to make AB C chocolates Will it take? ABC chocolate is being made every hour. So how many AB Cs are there in making chocolate? Will it take hours? So AB C AB C ABC Divide by. They will cut it. what will come Answer? That's what he must be doing. Not doing ABC These people. Suppose a company sells five chocolates every hour Makes it. How many chocolates will it take to make 20 chocolates? Will it take hours? 20/5 4 hours. So a company every Abby C is making chocolate. then AB C How many hours to make AB C chocolates Will it take? Divide it. By dividing them 1001 will come. Because above you see A B C ABC See, this is some algebraic multiplication. Not there. A B C ABC means ABC * 100 And this will be cut. What will be the answer? Let go If these six digit numbers are 5x2 y 6 z 7 11 is divisible by 13 then the value of x - y + 3z is Find out. Brother, if this number is 5x2 y 6z intersects 7, 11 and 13 Too. This means it will be deducted from 1001. six digits is the number of. So the one which starts with this number There will be three digits, the same as the last three digits Should matches happen or not? If you want to find this out then x y z Value is needed. The first three digits are 5x2 So the last one should also be 5 x2. 5x2 Should it happen or not? 5x2 means x value y of z then the value of x is six. five z of y of Two. 2 * 3 = 6 12 - 5 so the answer to this question is I have arrived. Did you understand, dear brother? Let go Let's move ahead. Any problem? Did you enjoy it? Okay, right? Next This is about ABC. A B C A B About C. And many more special numbers Are. You guys please understand it well. Ok Children? 101. What is the number? 101 101 all children If you listen carefully to 101, Multiply any two digit number If you add any two digit number of 101 If we multiply the two digits of 101 then What will be the result of multiplying the number? 101 * 73 so there will be repetition twice. First 73 multiplied by 100 will be 7300 + 73 What will come in one, 73, so if you Multiplication of any two digit number If you do it, it will repeat twice. Understand what I'm saying, like you did in 58 of 101. If we multiply 58 by what, what will we get? 58 58 58 Understand dear children I think If everyone has understood the matter then you tell me Tell me if a number is written like this ab ab which are the first two digits which are the same as the beginning has two digits and the last two digits are Otherwise, this means that this number will always From whom will it be cut? From 101 will it be cut if any four Number of digits whose first two digits are the same The last two digits are always 101. What will be the number that will be deducted ab * 100 ab * If you understood 101 then ab ab whenever you see ab ab If a two-digit number is repeated twice, then understand It will always be divisible by 101. Come on, come on. Do you understand this? You will say yes Sir, I understand. Okay, right? Similarly, suppose there is a number Special 1 0 1 0 1 0 1 0 1 0 1 0 here Look, one then 0, 1 then 0, then if you look at this You will multiply by a two digit number. I Took one for example. If you make this If you multiply it by any two digit number Tell me what will come after multiplying? 10101 that you will multiply any two digit number by So what will come after multiplying? 64 * 1 = 64 64 * 1 = 64 64 * 1 = 64 means dear Children write this two-digit number three times. It will be repeated. 64 64 64 I understand Children? Remember the special case 1 0 1 0 1 1 0 1 0 1 If you enter 0 in any two digit number If we multiply this by a two digit number It will repeat three times. I understood Dear children? Is it clear? like you Multiply 100 by 1001 In which? Multiply 70 and you multiply by 1001 You can do it in 32. On multiplying by 32 What is? 32 32 32 Got it? Now the opposite is also understand. It is very important to know the reverse as well, isn't it? Because the questions come in reverse. Let's assume A number of six digits is written in this In a proper way. ab ab ab ab ab ab ab ab This is a six digit number Is. But only two digit numbers can be divided into three It was written by repeating it several times. ab ab ab so this What will that number be? a b * 1010 This number will always be divided by ab. ab multiplication What will happen? 1 0 1 0 because ab is equal to ab ab Ekam ab ab Ekam ab if you don't understand children then if A six digit number is written as ab ab Now who will cut this? 101 So it's okay kids, let's ask questions like this CGL 2022 Pre came in ab ab ab Six digit numbers of the form always begin with It is divisible if there is a six-digit number The number is ab ab ab so you should understand It should be a two digit number. There is repetition three times. So this is what it means that this ab * 1 0 ab ab ab will come. So this number is always 1001 divisible by Will happen. Did you understand? Option number D We Did you understand everything? any problem Is it not true? Let go This number is 100101 This is a very special number in itself. As You know 1001 1001 I just told you Read 101 is a special number. 7 * 11 * 13 This 1001 is also a very special number. On this Not many questions have come up. But I I will tell the examiner that the examiner Brother, please learn and make a question on this. You will enjoy it. Okay kids? So attention Listen to it from. I will write down four prime numbers for you. Am. 3 7 is not 13 and 37 is not 11. 3 7 13 and 3 7 13 37 3 7 13 You can multiply them on your mobile. multiply by. What's coming? 3 7 13 and 37 You multiply them. Multiplication in your mobile This is what will come of it. 1 0 1 0 Did you come? These While playing, the man came to know that friend 3 7 What will happen if 13 is multiplied by 37 Multiply by 1 0 3 * 7 * 13 * 37 1 isn't it and this 101 is such a special number that if It should be multiplied by any two digit number For example, consider a two-digit number For example, if 6 7 is multiplied by 67 then What will come? 67 * 1 = 67 67 * 1 = 67 67 * 1 = 67 means two digit number Khatak It will appear before you three times. Isn't it? So You can also understand it the other way around. This means if It is written ab ab ab ab ab ab meaning What? a b * 1 0 1 And 1 01 is 3 * 7 * 13 * 13 Meaning a number of the format ab ab ab is also greater than ab This number will always be cut even by three It will be cut by seven, it will be cut by 13 and this It will be cut even by 37, tell me did you enjoy it or not, okay? Isn't it kids and this is what the question has been asked about Look at this as it is from the previous year. There is a question. Make it a little. Ok? Everything is going well Sachin sir. x and x and x and Consider a six-digit number of the form I stopped thinking that very day. When you were born, the number was divisible by tell me xy xy xy Dear children, this is it xy xy xy This is the same. Three of two-digit numbers Repeating xy xy xy what does it mean will be? xy * 1001 xy * 1001 That is 3 * 7 * 13 * So this number will be cut from all dear children. Isn't it? 36 The word only should not come. only Should not come. Only means only seven and 13 Cut from. Don't get separated from anyone else. So the answer What is? 3 7 13 End Got it kids? I think all the kids understood. D Option This is the answer. Ok? Let's go with this one Let me tell you the last concept. the question is No, it is not necessary but you must understand the concept. Know it. See 37 * 3 is 100 11. It is special. Isn't it? It is also used in calculations. 37 * 3 = 100 Remember 37 * 3 = 111 Now multiply 37 How to multiply 24 by 37 * 24 You immediately think 37 * 24 24 means 3 * 8 = 3 * 8 = 24 so 8 of 37 * 3 = 111 Multiplication means triple 8 I tell you 37 * 15 15 means 3 * 5 = 15 37 * 3 = 111 * 5 = 5 5 or not kids? So you can understand If any number is in triple A format has done. Isn't it a single digit? Write a single digit by repeating it three times. Given triple A triple A so it means that this number is your triple A a * 100 is 11, right brother, like the meaning of 555 what is 5 * 100 11 and 111 is 37* So this number will also be deducted from triple A 37 and I understand, dear children, there is no problem. what is it saying We Let's go with this divisibility rule here. completely It ends. ok full number of the system The most important thing in the entire number system Divisibility rule exactly I squeezed He kept it and taught it in such a way that even after taking money Teachers do not teach. ok my brother It's over, let's move on Now inside the number system in front of you The next type that will appear in front of you is type number two. Or what should I say next, say the next portion okay my brother let's have a lot of fun It will come, listen carefully, it is very small It's like we'll finish this very soon. Dear children, listen carefully. all the children My brother, if you have a number in front of you It is given in this format a to the power n + b to the power of n if you encounter a number like this The format is given as a to the power of n + b power n or it could also be a to the power n - b to the power of n plus can also be and We have to see about the minus also that this Number written in this form Number written in this form number reached Is it divisible by a + b or a - b Does it divide? Listen carefully. On this The question comes after targeting. be careful Please listen. If a number is given in front of you Hey dear friends, this is how the power of a a to the power of n + b or a to the power of n - b Power n where a b and what is this n? will be integer. will be an integer. What will happen? Integer. Pay attention, same power at both places Will happen. There should be n here too. here also n Should be. So such a number is either a It is cut by a + b or a - b. This is what to see Who will it be divided with? Now there are four cases here. Are made. Understand it very well. of a power n + b to the power n. It is also written here to the power of n + b to the power of. But both the numbers are written the same. Listen carefully, dear children. Both The numbers are written here. But This is the difference, dear children. This is also a is n to the power of n + b. And this is also a to the power n + b to the power n. But here is power n odd. Power n even here Is. Understood children? Let's take the second one here See. This is written as a to the power of n - b Power n number. It is also written here that the power of a n - b to the power n number. But the difference is that Here power n is odd. This is even. Ok Children? Let go If a number is of the form a^n + b^n It is written by. If a number is placed in this way It is written in this format a to the power n + b to the power of a to the power n + b to the power n if Power is odd. Power is an odd number. Power Either one, three, five, seven, nine Yes, it is 101. In this way if the power is odd So this number will always be divisible by a + b But a will never be divisible by a - b. These The number will always be divisible by a + b but will never be divisible by a - b. You How will you say sir? You can enter any odd number in place of n. Keep the value. You can replace a here with n. Keep the forest. Look cut off by a + b. You n's Place three. a + b then a + b also has a There is a factor. a + b a + b formula What is? a + b * a² - ab + b then a + b a + b also comes inside. so deep in You don't even need to go. this memory Put if a number a to the power n + b Power n is written in the form. Power if odd. Odd means one. instead of n Make it a forest. So this number is will be divisible but not divisible by a - b Will happen. Did you understand, dear children? This This number is a to the power n - b in this way. What is power n in the middle? If the power is odd, power an odd number. You Replace n with any odd number. Like forests. So what will this become? a - so this will be divisible by a - b. but from a + b Divide this by the number a to the power n - b to the power of n if to the power odd if to the power So this will always be divisible by a - b but a + b will not be divisible by a. Understand this a to the power of n + b to the power of n if power even Is. Even means two. You put two here. See. a to the power of 2 + b to the power of 2 is this Breaks ahead? Does this constitute a formula? Is there anything ahead? No. That is, this number is neither a It will neither be divisible by a + b nor by a + b This will never be cut by a - b. So on this There are never any questions. Got it? Understand this. If a number is written as a to the power n - power of b if a number a is raised to the power n - b to the power n. If power if power n even Is. If the power is even, dear children, then this a to the power n - b to the power n even means What happens? Two a² - a² - b² mean a - b * a + then this number is also divisible by a + b and also from a - b. Divided by both Will happen. This number will also be divided by a + b and a - b It will also be divided by. Understand it well, my love Children. These four cases are made. If a number is The power n + b to the power n is written as. Where the power is an odd number, it is always a + will be divided by b. That is, from a + b On dividing, the reminder will be zero. of a power n - b to the power n if the power is odd This number will always be divisible by a - b. a to the power of n - b to the power of n if the power is even. Even means keep two. If two are even numbers then It will intersect a + b as well as a - b It will be cut. Let me explain the example now. From. a to the power n + b to the power n if n to the power a It is an odd number. Odd means keep one one one. So That is, it always has a factor a + b will be. That is, if you multiply a to the power n + b If you divide power n by a + b then a + The remainder will be given by dividing by b. If you divide by a + b then dividing by a + b But the remainder will come. But when? if n is a power It is an odd number. Did you understand? like tell it 27 to the power of 39 + 11 to the power of 39 by 19 What is the reminder when dividing? This question comes Went. 27 to the power of 39 + 11 to the power of 39 ok? Dividing this by 19 What will the reminder be? This is your question In front, right? 27 to the power of 39 + 11 to the power of 39 Anyone understand dividing by 19? be careful Please listen. Now tell me, dear children. I can say that this is a to the power of n + b Power n is of format. a to the power of n + b Power n What is power here? 39 It is an odd number. Power is an odd number. So this a to the power n + b to the power n The number is always a + b i.e. 27 + 27 + 11 This means that the number 38 is always divisible by 38. Will happen. 27 to the power of 39 + 11 to the power of 39 Will always be divisible by 38. Divide this number by 38 If you divide by then the reminder is exact Zero will come. But I'm asking 19 What will be the reminder on dividing? If If this number is divisible by 38 then 38 is the only child of 19 if a number is greater than 38 If it is being cut then the factor of 38 is 19. From 19 will also be divisible and on dividing by 19 What reminder will come? So what? Understand My brother? Tell me any problem? Correct? Ok. Come on, that's it You have to know the concept and questions come on it. In the paper before you. Let's take a look at the CGL Mains This is a question from the 2020 paper. Absolutely beans To the same as it is. Tell. 127 ^ 97 + 97 ^ 97 divided by 32 If 1000 is added, what is the remainder left? Tell me. 127 to the power of 97 Isn't it? + Power of 97 Power of 97 divided by 32 How much remainder is left? So you understand. First Look what form this number is? of a^n + b^n + a^n + b^n and here power Which is what is 97? 97 is an odd number. If written as a to the power n + b to the power n. Power is an odd number. So this number is always a + b will be divided by. This number always What would be a factor? a+ a + b means 127 + 9 What is 127 + 97? This means that this number is always divisible by 224. Will happen. If this number is divisible by 224 If it is there then it will also be reduced by a factor of 224. Asked to divide this number by 32 But what will come? Is 224 being cut off by 32? What does 224 mean? 32 * 7 means 224 32 * 7 means If this number is divisible by 224, it The number will also be divisible by 32 and If you divide seven by 32, you get 32. What will be the remainder after dividing if it is 0? The answer to this question is 0, don't you understand dear? children Clearly, when you know the concept, a to the power of n + b to the power of n if b is odd So this number will always be divided by a + b Come on, tell me this 73 to the power of 53 + 83 to the power of 83 to the power of 53 Is it divisible by what is it divisible by? These The number is given. This too in CGL in 2020 Had come. What is this number divisible by? Tell You will see 73 to the power of 53 + 83 to the power of What is power? Power is an odd number. Is it or not? If here Power It is ode. It is of the format a to the power n + b to the power n. So this number will always be divisible by a + b. a + b means 73 + 83 i.e. 100 The number will always be divisible by 156. Answer What will come? B option. Tell me this children. 8 Factor 2k to the power of 2k + 5 What will happen? where k is an odd number. k is an odd number. Tell me children What is the factor of 8² 2k + 5² 2k? where k is an odd number. Tell me dear child. Now Look, we have to factor them out, k is an odd number. Is. If k is odd but odd is multiplied by two What will happen if we do it? Even. and a^n+ b to the power n if the power is even then any The concept is not formed. Neither a + b will intersect No. So brother, you will have to work hard in this. Good question. 8 to the power of 2 is like 8 to the power of 2, so I can write it like this Am. 8 to the power of 2 is not the square of 8. Its hole power k. This is 5 to the power of 2. I can write this as the square of 5. Hole power k. Now you know that 8 Square 64 to the power k + 5 to the square of 25 25 to the power k so I can say 64 power k + power of 25 I had given this number but I changed it like this This becomes a to the power n + b to the power n where What is power k? Power k an odd number Is. It is an odd number. and any number if a key written in the format power n + b to the power n then this number is always divisible by a + b + b means 64 + 64 + 25, that is The number will always be divisible by 89. So the answer What will come? D 89 This was the thought that Here you get a to the power n + b to the power n I have to write. Okay kids? Let's move ahead. it Tell. 3 to the power of 41 + 7 to the power of It is 82, isn't it? From what will it be divisible? These four The option is in front of you. Tell We 3 to the power 41 + 7 82 in all four options From what is it divisible? You tell. wrote this This is 3 to the power 41 + 7 to the power 82 The problem is that power 41 here power 82 here Is. The problem is, is there power in both these places? should be same so 82 means 41 * 2 So 7 to the power of 82 can be written as 7 square of to the power of 41 to the power of each other I will multiply it by 41 * 2 = 82, so 7 What is square, it is the power of 3 41 + 7² 41 to the power of 49 now becomes the same as a to the power of a what is n power to the power of n + b to the power 41 to the power If an odd number is odd then this number is always even will be cut by a + b. a + b means 3 + 49, so This number always Will be deducted from 52. If this number is divided by 52 If it is happening then the factor of 52 is not 10 Yes, it is not 51, it is 26. If this number is 52 If it is divisible by then it is also divisible by 26 It will happen. This answer has come. Isn't it? Excellent Tell me the question. 5 to the power of 70 + 7 to the power of What is the reminder when dividing by 37? will be? a to the power of n + b to the power of n What is? Even this will not be divided by a + b. from a - b. Then the question will not be solved. So how will you do it brother? 70 means 35 * 2 70 35 * 2 = 70 so 5 to the power is 70 Children. It cannot be written like this. Five Square of its hole power 35 to the power of 7 is 70. It was not written like this Can go. square of 7 to its power 35 You will say sir, the square of 5 is 25 25 The square of 35 + 7 to the power of 49 is 49 You can understand the power of a yourself, this is a to the power of n + b to the power n became the same format. Power What is? If the power is an odd number then this number is a + b Will be divided by. A factor of this number is a + b will be. a + b means 25 + 25 + 49 74 This number will be divisible by 74. from 74 If it is being divided then it will be divided by 37 also. of 74 It is a child 37 74 What happens? 37 * 2 = 74 if this number is divisible by 74 So it will be divisible by 37 and divisible by 37 You will get a reminder to tell this to the children. 756 to the power of 273 - 412 to the power of 273 - 86 how much reminder is there if it is divided by Is it left? Now you see a to the power of n minus What is n to the power of b but the power? Ode. Now! explained a to the power n - b to the power n is The format is written. if n is a power It is an odd number. So a to the power n - b to the power n always from a - b It will be divisible. Always from a - b. So this is a to the power n - b to the n power odd. So It will always intersect at a - b. Meaning of a - b What is the result if you subtract 412 from 756? 300 is exactly divisible by 344 Will happen. 344 But asked what if it is divided by 86 Will you come? What does 344 mean? 344 to 86 If this number is subtracted from 344 then 86 is multiplied by If it is being cut, then 344 has a child, even from 86 86 What will be the reminder on dividing? is 0 No question? Tell me this. 97 to the power of 30 - 14 to the power of 30 Tell me it is divisible brother Are you having fun kids? 97 to the power of 30 - 14 to the power of 30 Is it divisible? It has come brother. Look at the attention Listen to it from. a to the power of n - b to the power of What is Power 30 here? one power one even There is a number. Even means two. if the value Let us put two in place of n, then a² - b² This number will also be divisible by a - b and a + b b is divisible by both a - b and a + b This number. So if 97 to the power of 30 - 14 If the power is 30 then this number is a - b i.e. 97 - How much is 14? It will also be divisible by 83 and 97 + 14 97 + 14 That means 100 It will also be divisible by 111. So this number is 83 will also be divided by and So tell me what will come? C option will appear. If this number is divided by 83 It is dividing and 111 by 111 means 37 to 100 is also greater than 83 It is getting divided and it will get divided by 37 also. both ayega 37 end Isn't it a problem kids, let's go to 37 and 83 It will be divided by both. Let's ask the last question Type it in front of you. Two statements have been given before you. Isn't it? You have to consider these statements. Which is right and which is wrong. 67 107 to the power of 100 - 76 to the power of 100 Let's look at 67 to the power of 5 + 33 to the power of 5. Is 61 divisible by this number? What do you see here, dear children? Pay? It looks like a to the power n - b What is Key Power Power? If the power is even then this number is even with a - b will cut and What will come out to a - b? 107 - 76 31 And what is a + b? 107 + 76 means This number will also be divisible by 31 and It will also be divisible by 183. And what about 183? it means? 61 * 3 = 183 i.e. this number If it is divided by 61 then the first thing will happen. Isn't that right, kids? No problem. 100 divides this a to the power of n + b to the power of What is n power? If the power is odd, it means the number is a + b will be divided by. a to the power of n + b to the power of What does n a + b mean? 67 + 33 means This number will be divisible by 100. So What will be the answer to this? Both. Ok? Tell me. Tell me, is there any problem? Let's go with this type. also completely It ends. Let's untie the thread. Now Hewan Khede ji. Now the next type in front of you Comes. Which one is it? Next type Next concept. Number of factors. of factors It's quite long, but I'll read it to you. I will stay. Sachin is the number of factors. Do you understand? We will factor it in today. every Factor will play in the sector. Understood? Let go. Number of factors. one by one I love you so much and I am so comforted by this concept I will explain it to you that it will definitely stick in your mind. I will miss you my friends for the rest of my life. It will remain how the factors are calculated. First you should understand what factors are? Factors Suppose I have a number in front of you. Written 56. So, by which numbers should 56 be divided? But the reminder zero comes that 56 are called factors. That means 56 Jin-Jin All of them will be exactly divisible by numbers. What will happen? Factors of 56. like 56 one is divided by. You divide 56 by two Will go 28 times. Remainder zero. 56 more than four There is a divide. 56 from seven also, 56 from 8 also, also by 14, 56 by 28, 56 by itself 56 Too. Now should I ask you whether 56 is divided by 15 Will you divide by? 56 divided by 15 If you do it, will there be an exact divide? No. 15 * 3 = 45 What will be the remainder? That means 56 is not a factor of 15. So this There are lovely children factors. You notice to do. Every number always has a factor only occurs. every number is divisible by one Is. Every number must be a factor of itself Are. Because every number is divisible by itself it occurs. Did you understand, my brother? Any pain? Now here I will tell you about 56 How many factors are there in total? Count and tell me. So You will say Sir, count 1 2 3 4 5 6 7 56 There are eight factors. You counted them. Understand Children? But if I had a very large I'll give you the number and ask you how many of it are there. Will it be a factor? So you can count it this way You won't be able to tell, right? Then we need a method We should look at the shape of any number. can you tell me how many factors it has And that is what we have to learn in this type. Understand No? So let me start with the concept first. dear children and after that you will have fun Will come. Come on, listen carefully my brother. Ok? please listen Carefully. For example, I used your I wrote a number 72 in front. small number Let's take it. Small numbers will make sense to you. Will go. For example, I have presented it to you Wrote a number 72. We have to say that 72 How many factors does? Total of 72 How many factors are there? Understood dear children? You will say yes sir. So whatever number you get Given, you do its prime factorization. What to do? Prime factorization. you will say Sir, what good is this? Prime Factorization Do it. That is, by breaking the number Give it. Break the number so that the base is always Stay prime. Numbers into prime numbers Please brake. Like what is 72 72 Dear children? All the children know this. 72 equals 8 * 9 72 but eight so break even further will be. What is eight? two and then some can not write. Eight to two is 1 and 2 only Will remain. What can we write for nine? of three You can't write the square of three further. Any. Three means 1 3 so this is 72 Prime factorization. where base two and three What is? are prime numbers. I understand dear Children? So whatever number you've been given You have to do prime factorization. Did you do it? You will say yes sir. of the factor What does it mean? Child of numbers. of the factor What does it mean? The child of the number who is divides the. 72 has two children I can see them clearly. one of two Cube and a square of 3. Now two Cubes can also have many children. Or not? Cube of 2 means eight. of 2 What does cube mean? eight from whom Does it divide? Eight. 8 divided by 2 Power 0. Look at any number of If you do power zero, it means One. Cube of 2 means eight from which Will it divide? So eight divided by the power of 2. 0 means from forest. Eight divided by 2 Cube means 2 to the power one. Eight divided by 2 to the power of two is four. The cube of 2 will be divided by eight, that is Himself from eight. That means if I raise 2 to the power of 3 If I pay attention to 2 to the power of 3, then four The factors are to the power of 2. That means if 2 to the power of 3 is then to the power of 2 from 0 to 1 2 3 All these will become children of the power of 2 that Won't you make it? Will it be made or not? That is, if If there is a power of 2, then the children will go to the power of 2 of 0 to the le power three. 2 to the power three eight If it is there then it will be cut by one, by two, by four And I understood it like this, now you see what this is. The square of three means nine times three. Square means nine. Now tell me what divides nine into. It happens that nine is divided by one, three is divided by one Meaning it is the square of three, right? What will cut the square 3 to the power 0 to one to 3, that is, the square of 3, that is, nine. You will say, yes sir, absolutely right. One Just multiply them times. What to do? Multiplication. You just multiply them. Hear Multiplication to do. What did I write, dear children? be careful Please listen. I am writing in front of you. 2 0 to the power of 2, 1 to the power of 2, 2 to the power of 2 and 2 to the power of three. What are all these? Power of 2 Three children. What are the children of 3 to the power of two? Is? 3 0 3 1 3 I'm multiplying them while you multiply them If you do, just listen to 2 to the power of 0, that is 1 1 * 1 * 3 0 1 1 * 1 This is a multiple of 1 72 is the factor. 2 to the power 0 1 1 * 3 3 a factor of 72 Is. 2 to the power 0 1 * square of 3 9 72 is the factor. Do you understand? Enjoying it Is? 2 to the power of 1 1 * 1 * 2 to the power of 1 2 * 1 = 2 2 is a factor of 72 2 to the power 1 2 And this is 1 to the power of 3, that is, three 2 * 3 = 6 is a factor of 72. Square of Two Sorry 2 1 to the power of 1 and the square of three is 9 * 2 18 is a factor of 72. Is it or not? of 2 Square four 4 * 1 = 4 a factor of 72 Square of 2 is one of four 4 * 3 = 12 72 The square of 2 is the factor of four and three. Square 9 4 * 9 is a factor of 36 72 And what you're left with at the end is 2 to the power of 3 means eight is a factor of 8 * 1 = 8 8 72 cube of 2 is a factor of eight 8 * 3 24 72 and finally the cube of 2 is 8 and that of 3 squared 9 8 9 72 which is a factor of 24 Is. So what did all this 72 bring? Other than this Any number that divides 72 Keep groping throughout your life. The world will not be found In. Will I get it? That is, the more times they The same number of factors multiplied together Will become 72. As many times as they have The same number of factors will be formed for 72 when multiplied. And How many times will this multiplication take place? That is to think that How many times will it be multiplied? Total number of 72 How many factors are there? How many times will it be multiplied? So you think this was 2 to the power three. 2 of Power became the child of three. power 0 power of 2 1 to the power of 2, 2 to the power of 2, that is, power If there were three, how many children did they have? One child is too much. Why? Because There is also Power Zero. Understand? two to the power of three Was. So how many children were born? two to the power of three Three of. The power was two out of three. Power of three There were two. So one more child than two Dear children. And when I talk to each other If I multiply, how many Will there be combinations? There are four of these and three of these Are. These are four and these three are among themselves. If I multiply them, how many will be the result of multiplying them? Will there be combinations? 4 * 3 = 12 i.e. 72 How many factors are there? There are 12 factors. Tell me any problem? Did you come? Did you enjoy it? completely opened up I have. So if for any number you get If you want to find the number of factors then understand Here you go, do its prime factorization. Done prime factorization. as much power Multiplying by one addition will be Is. How much to add? Why do it? There is no need to memorize. has explained I have. Isn't it? because 2 to the power 0 is 3 Power 0 Power 0 comes with an extra. Understand No? Here comes the method of finding the factor. If Suppose I had asked you about 72 What is the sum of the factors? factors of 72 What is the sum of the sum? So 72 What is the sum of the factors? So brother 2's All the children of Power were written down. 3 to the power of 2 I wrote down all the children. If among these A plus should be added. what did you put Should I go? Put a plus in between these So brother, these will keep multiplying and this Additions will continue. These will multiply and All these factors of 72 will add up. So What will come? of factors of 72, that is Finding the sum of the factors of a number Of. So write all the children and do what? Multiply it by plus two. Is it or not? This one It became a general concept. Of a tiny little I explained with an example. But every question Will be applicable in. Whatever it may be. I enjoyed that No? Wankhede ji? Did you enjoy it? Ok. Let go Now, like 72, let me ask you about 72. What is the sum of the factors? So 72 What will be the sum of the factors? First prime Do the factorization. Cube of 2 * 3 is 2 I wrote all the children of the cube. All the children of three squares, all the children Meaning from power zero to two. Now tell me this cube of 2 8 4 12 two 14 and one 15 And how much will this cost? Square of 3 is 9 3 12 one 13 What will this 15 * 13 become? came early Did you not understand it, you will say sir it's fun My heart has come, it has become like a garden, okay So I took this one small one, if I take a Let me give you a big example, listen carefully now. The real fun will come, okay? I took a number in front of you 2160 very 2100 is a good number. What are the total factors of 2160 and the factors What is the sum of Rs? This has to be told. So first You tell me the prime factorization of 2160 What is? Look, we have to break it a little. What comes in 2160? 2006 216 is the cube of six multiplied by 10. Went. What does six mean 2 * 3 = 6 Is? 2 * 3 6 and its Cube means cube multiplied by 2 Cube of 3 and 10 means 2 * 5 = 10 Went. So you can see how much two Will there be power? 2 to the power of three and two. 2 of Power of three cube of 3 and this This will be five. So I can say 2160 I wrote down the prime factorization of 2160 is the power of 4 * 3 * 5. How many factors will there be in total? So I Taught to do prime factorization. Ahead So it will not break. So whatever power there is, power Only with the multi power of one addition can children Are made. The greater the power, the More children will be born. Multiplying by Factors Let's come. Isn't it kids? So one in power Multiply by adding. 4 + 1 3 + 1 1 + 1 and 5 * 4 = 20 * 2 = 2160 There are 40 factors. Did you understand? be asked What is the sum of the factors of 2160? So 2 of have power Four. So starting from power zero. 2 of 0 to the power of 2 1 to the power of 2 2 to the power of 3 2 to the power of three is three to the power starting from zero power of 3 0 power of 3 1 to the power of 3 2 to the power of 3 5 to the power of one So starting from zero is 5 to the power 0 and 5 What should you multiply the power of and all this? Do it dear children, will this happen? to the power of 4 16 8 24 4 28 two 30 and one 31 What is the result of multiplying 27 9 36 39 1 40 aa gone and how much is that dear children five more One So 40 * 6 will become 240 * 31 my brother 7400 is the sum of all its factors. 7440 744 0 I understand, dear children, is there any problem? Boys are having fun, let's move on Dear children, now from here Will not get it done until the entire concept is together When he makes a child, Let us now look at the number 2160. Meaning of 2160 2 to the power of 4 * 3 3 * 5 1 is prime is factorization. Now there are many types of factors. Can be of. Factors can be even Yes and odd too. So you can also ask this How many factors of 2160 are even? Ask this also How many factors can 2160 have? It's easy. Imagine if you have in front of you Given a number and asked for 2160, like 2160 How many factors of odd are there? Number of Odds Factor the odd factors of 2160 what is the number? How many factors are odd? What does odd mean? Odd means two Multiples should not come. two don't come Needed Two should not come. So this is from 2160 is prime factorization. Power of two in this What comes? Any number of two to the power of four All who are multiples of two will become children Will it happen or not? So baby, you have to take this. Not there. What do you just need to pay attention to? On their children. That means only you Had to find the factor. Is it or not? I understood In? So you just have to factor it out. So 3 to the power is three so one to the power Will add. 3 + 1 or 5 to the power of one is Will add one to the power. 1 + 1 And how many of 4 * 2 = 2160? Odd Factors Are. Eight. Did you enjoy it? The odd factor of 2160 is eight. Total Factor Are. The total factors of 2160 are 40. So what will be the remaining factors? Even means how many even factors? 2160's 32 Let's go now, don't worry here either. Let's ask the sum of the odd factors of 2160 What is? Isn't it? Odds factors of 2160 Isn't it? of odd factors sum. of odd factors sum. So brother odd factor means you You should not buy goods with power of two. Only this is what its factors will be Find their sum. 3 to the power of three was So power 0 power 1 power 2 power 3 power of 5 1 was 5 to the power 0 to the power of 5 this will come Dear children, 40 and it will come So 40 * 6 equals 240 and the odd factors of 2160 The game is over, you both learned, did you enjoy it now? Suppose the question comes before you that What is the number of even factors of 2160? how many even factors What does even mean? What does even mean? Wankhede Ji Do Ka of two Even means multiple of two. Multiple of two What does it mean? That means this is the prime of 2160. is factorization. I only need those factors which is a multiple of two. at least of which What do you know less? You may come twice once. two of There is no problem if you come more often. So if What do I need for 2160 only? Even Factors. So brother, this is what you get prime Factorization is where you first take out two Take it out. What did you take out? two out Take it out. That means if you take out two What will come? 2 to the power of 3 multiplied by 2 to the power of 3 5 to the power of one. So this is the stuff that Dear children, this is the stuff of Listen to whatever factors come up. This one Whatever factors come into play for the goods That should be multiplied by two outside, at least for everyone. What will everyone be like? Will be even. That means that I Only its number of factors have to be found. No. And find its number of factors How to add power to a device and push it Multiply. Is it or not? You wrote this, right? What will you do with two? Take it out. Only Find its factors. What are its factors? Will it be? One added to the power 3 + 1 3 + 1 1 + 1 4 * 4 = 16 2ni 32 see 32 will come 32 even Eight odd total 40 understand na mast hai sab relet There is one concept that ends everything If asked about the even factors of 2160 What is even? Sum of even factors is even Sum of factors is even means less than even means Less Power of 2 Minimum 2 to the power of one i.e. 2 to the power of 0 Isn't it like you listen carefully like 2100 You see here in the case of 72, these are 2 What is 0 to the power of one multiplied by three? If it becomes three odd factors then if it is If I, the father-in-law, end this affair, What will happen if all this is multiplied by two? Will it become an even factor or not? So if you 2160 or any other number, its even The sum of the factors has to be found. Even means at least least power of 2 least power of two Forest. So these would be the children of 2 to the power of four. Are. 2 to the power 0 1 2 3 4 so 2 to the power 0 Don't take it. I have to start. At least 2 to the power of 2 then to the power of 2 to the power of 3 2 Power and all this will remain the same. Will your answer come? Will you do it for 7200? Did you understand, dear children? Mr. Wankhede? Any doubt? 2 to the power of 0, because 2 0 to the power of one. One's Ahead Odds Numbers can be multiplied to form odd factors Are. He finished the game. Got it? Did you enjoy it? Ok? Let's move ahead. See how lovingly I explained it to you. how deep Hey, this is all junk. Brother, you are 50 years old. Haven't gotten it liked yet. Are? Are you reading it? I am enjoying. The students went to buy oil. I am enjoying. Correct Yes sir. Let me enjoy. Go to Hell. ok sir. Let me teach you this or that. I'm teaching to make myself happy. Understood? Your work is being done. Ok. Yes. Don't be too pampered. Understood? 2160 Suppose we have total number of 2160 Factors were also taken out. Find the even factor For. Odd factors were also removed. Now The examiner becomes very hot. He says, son, tell me the factor of 2160. Which is divided by 12 or tell me the factor 2160 Those which are deducted from 18 or those which are deducted from 2160 Factors that cut through 40 Ask anything I can ask anything, I can understand one thing If you do everything after covering yourself then it will seem as if there is someone in front of you. Number 2100 This is the prime factorization of 2160. We need to find the number of factors of 2160. I have to tell which is a multiple of 12. 12 means that the number of factors that are multiples of 12 2160 such children who are cut off from 12. As How much is 12 24 36 in this way? What Are you asking? 12 means 12 Square of Lovely Kids 2 4 * 3 is exactly 12. So this is from 2160 is prime factorization. 12 out of these Take it out first by pulling it. So 12 out What will come if I take it out? Square of 2 Multiply 2 squared * 3 i.e. 12 I Took it out. So what will be left? Power Four If it was there, what would be left? The power of 2 was three. What will be left if there is power of three? Power of three And five more. So this stuff has as many children as it has All this stuff that is outside will be multiplied by 12. What is happening will be all 12 that is All you have to do is count its factors and How will the factors here come into power? Add up and multiply 2 + 1 2 + 1 3 and 1 + 1 so total factors of 2160 The factors of 18 2160 which are equal to 12 Multiple is what happened are cool and and The sum of the factors of 2160 which are divisible by 12 It is multiple. All those factors cost 2160 Add and tell me which are subtracted from 12. Otherwise I will cut it. So brother, the 12 that is to be subtracted from 12 Meaning 2 squared is four and 3 The square of 2 is four and thia is 12 12 ok sir. So at least 2 to make 12 What power is needed? And what is the minimum power of three required? One. If there is more power than this then it will be fine. Like 2 It will be fine if the square of 3 becomes the square of 3. But what is the minimum required? 2 to the power of 2, Power of 3. So this is the prime of 2160. is factorization. Here we must begin Is. You need multiples of 12, right? that factor Those that cut through 12 are needed. So let us begin At least 2 to the power of two. at least 2 to the power of 2 should be 2. So 2 to the power of 4 Which factor is it? 2 to the power of 4 is also four It cuts. 2 3 to the even power of 2 2 to the even power 1 to the power of 2 to the power of 0. But What is the minimum you need? to the power of 2 We have to start with 2² 2. 2² 2 of 2 4 these Will add. What is the least power of three? Needed? 3 should not be raised to the power of 0. Because at least three must come out of 12. Times. So let's start with 3 3, right? 31 3² 2 to the power of 3 times five So there is no meaning. 5 0 + 5 1 will do this These 28, these 39 and these 6552 Did you understand? Is carefree. That's all you need Have to understand. Now ask a quick question Show me and you think If this question is asked in GD paper then what It should be done. Whom? The sequence is not formed. Will show. Total positive factors of 10,500 What is the number? How many total 10,500 Are there factors? Tell. How many factors does 10,500 have? So We are not such that we can count and complete everything. We will keep counting them in the locality. So What should you do with 10,500? Prime Factorization. What is 10,500? Thinking You will have to, dear children. 105 * 100 understanding I came? 105 means 21 * 5 = 105, 3 * 7 = 21 and pawns 100, 100 means 25 * 4 = 100 i.e. 2 Square * Square of 5. This is 100. I don't I think I can break through this. So here The square of 2 came. Multiplication 3 has arrived. Multiplication seven came. five of How much power did you get? 1 to the power of 5, 5 to the power of So here it comes. Three means 3. Power one. Seven means 7 to the power of one. What is it Have you arrived? Prime factorization. Have you come? Correct? Any problem? So tell me how much of it Will there be factors? So add one to the power and Multiply it. 2 + 1 3 1 + 1 2 1 + 1 2 and dear children this 3 + 1 4 3 * 2 = 6 * 2 = 12 * 4 = 48 option numbers B 48 is okay, right? Let me tell you. How many primes of the number 840 are there other than one and 840? Are there factors? Understand and tell me How many primes of the number 840 are there other than one and 840? Are there factors? So you should find out in advance that How many factors are there in total for 840? Isn't it? So What is 840? 21 * 4 brother 840 means 84 * 10 84 means 21 * 4 = 84 i.e. 3 * 7 * 4 means square of 2 and 10 means 2 * 5 10 It's here, isn't it, dear children? Any pain? 21 * 4 = 84 and 10 means 2 * 5 = 10 So what is the total power of two? So 2 of Power 3 * 5 can be written like this. 2 to the power 3 * 5 So what happened quickly? Prime Factorization. 3 1 7 1 2 3 5 to the power of one. So you tell me the total number of 840 How many factors are there? Which we will call tnf. What will you say? What is the total number of factors? Tell me just. So the power will add one to one, in one Will add one. Two will add one to three If we add one to four and one, we get 2 4 * 4 = 16 The total factor of 2 ni 840 is 32. 32 Don't answer in a hurry. have asked Factor one of 840 and 840 Total factor of 840 is 32. You know every A factor of a number is one and the number itself It definitely happens. So two of these 32 factors The factors are one and 840. Don't take these. So what are the remaining factors? 840? There will be 30 factors left. that is No, my brother? It was a very simple question. These will tell do it. We 5 to the power 13 + 5 + 5 11 + 5 to the power 10 This is the value of n. asked for the number n How many positive factors are there? Isn't it cool? Question? Tell me please. If n is equal to this, then tell me the number n How many positive factors are there? So power 13 12 11 10 If we find the factors of this number then First of all it has to be primed Factorization. It is in its own unique tune Is. So what do you do from here first? 5's Power 10 is the lowest, isn't it? 5 to the power of 10 you You can take common. Will you take it? What will be left? 5 If it is 13 then the cube of 5 will be left then 100 25 was 5 What will be left? 5 10 common took 25 5 11 was 5 10 common took five and 5 5 out of 10 If you take 10 common then power of 5 10 how much is this 125 250 and 155 a 100 became 156 what would have been 156 is 12 * 13 12 * 13 12 * 13 taught 12 * 13 So it should be known that 156 means 12 * 12 means 4 * 3 = 12 so square of 2 is 4 * 3 = 12 and multiplied 13 Do you understand what I mean? Is it or not? What has happened? Prime Factorization. So how many factors does n have in total? Are? of the number n. One more addition to the power Multiply it. I will add one to 10 and get 11. Two I'll add one to make three. I'll add one to the forest Two. And if I add one to one here, the number tnf total is the number of factors of n The number of factors is 11 * 3 = 33 * 4 = 132 That means which option is 130, understand this. Let's understand the matter, we will read it at night. Come Are x + x² squared + 76 768 where x is a positive number. What is? Positive number. x which is a This number is exactly divisible by x. Okay kids? So I have asked the number of all The true value of x. How many values ​​of x are possible? Listen carefully. You are given a number x + x² + 768 where x is a positive number Is. x + x² + 76 8 x is a positive number. And this number is exactly divisible by x. Is. That is, if you multiply this number by x If you divide, then dividing by x The reminder will be zero. Tell me, is it true? Correct Isn't it? So you tell me if you can change it from x to On dividing, the reminder will be zero. So Asked what is it? The Number of Such Possible Values of x. How many values ​​of x are possible? how many of x Is the value possible? x + x² + 768 is exactly divisible by x. Tell me about 768 How many values ​​are possible? If you multiply this number by x If we divide by then it will be subtracted from x Will go. This will also be intersected by x. That means that This 768 is also divisible by x. Only then this The whole number will be divisible by x. That means that 768 is also divisible by x. That is, what is x Will it happen dear children? x is a factor of 76 8 Tell me, did you understand the matter or not? in question The question is how many values ​​of x are possible. So There are as many factors of 768 as there are of x. Values ​​will come. 768 numbers from which What will happen if it gets divided? of x. So It was an indirect question. How was it? Indirectly, how many factors does 768 have? Tell me please. Is everyone tired? What does 768 cut off? Cuts by eight. Brother 8 * 9 72 and 4 8 6 Are. Eight is the cube of two and 96 is 16 96 Meaning 32 3 96 means 32 * 3 = 96 i.e. 2 Power of 5* 3 so this is 2 to the power 8 * 3 means three to the power of 3, so how many Bhaiya, add one to the power and eight more will be the factors. If you add one to one then how much is 9 * 2? Are there factors? Isn't it? Great question? I enjoyed doing it. Let's move ahead. tell me this dear Children, what is the answer? Cube of 73 - Cube of 40 - Cube of 33 There is a number. The number of its factors How much is it? Govind ji, if you ask this question So two momos from me to you. I have finished everything with momos and drinks. Hey my brothers and children, are you enjoying it? Is? Do you feel any lack of energy in me? Can you see it? Guruji read after eating dal and rice We are here. Very good sir, how much longer The class will continue until you close your eyes. Those people did not understand the mess. Is everything going well? Why has it just started? It's only 12:30 now The program is till at least 2:30 today. We Yes and If kids are you enjoying it, name it We should change it and do night classes with Gagan sir is Not 30 days, but 30 nights From tomorrow I am getting the children to write thumbnail changes. I am 30 nights with Gagan sir now night woh wali She is not a night, I understand that she is a student Sir I am Vikas Sharma so what should I do? Brother? Keep your growth to yourself. Are The total number of factors of this number is 73 Cube of - 40 cube - cube of 33. Any Find the number of factors of a number only when when the prime of that number is Perform factorization. Prime Factorization The number to be solved first Needed It will take you several days to solve it. Will take. This is a special case. We are the number Teaching the system. But look at the concept It happens in algebra. You should understand it well. If the sum of three numbers is 0 if a + b + c = 0 a + b + c = 0 then If a + b + c = 0 then a + b + c is always equal to 3a bc that's it 3abc If you look at this number 73 I can write - 40 - 40 as -40 Plus this -33 -3 can be written like this -33 Of So you see it as a + b + c If you look carefully, here are these three spinning wheels The resulting value is set such that the The sum of all three is 0. So this observational one The question was. Look carefully. 73 minus 40 And minus this 33 = So this will seem like the same concept. If a + b + If c is 0 then what should this a + b + c be? 3abc means 3 * 73 * minus times 40 * minus times minus Minus became plus Exactly 33 means 3 * 3 * 11 then 3 * 3 what will become of 3 Square Multiplication 11 * 73 times 40 40 means 8 * 5 = 40 8 * 5 = 40 i.e. cube of 2 is 8 and 5 This is prime factorization. We have torn our hearts into pieces. So, What is this power of everyone? Tell me how many factors Are? 2 + 1 3 1 + 1 2 1 + 1 one to the power Add and multiply. 2 3 + 1 4 and 1 + 1 then 3 * 2 = 6 * 2 = 12 * 4 = 48 then double This number has 96 factors. 96 Got it? Let go You must have understood. Tell me. Sum of all the factors of the number 19600 What is? Ok? I have already explained how to calculate a number Find the sum of the factors. Come on, it's yours There is homework. Answer me in the comments Don't even tell me after doing it, be satisfied later. Isn't it from? Tell me everything later by commenting. Because I taught you everything. Even factor, odd factor, even factor, such and such I taught everything. Got it? So let's go now We will go a little further. Please tell me this. The question of NTPC has come up. Do NTPC. Put it on charging, brother. Are you having fun or not, boys? Sir ji greetings in the air from Bareilly. It is hot in Bareilly. No greeting from People from Bareilly. How many even factors does this number have? Even factor means it must be a multiple of two How to find out at least how many even Factor 2 to the power of 7 by pulling the first two Take it out, do you understand how to even the factor? Even factor is calculated, meaning at least 2 to the power of one so two to the power of 2 one out take it out, take it out, if I take it out If I take out all this stuff, it is All the factors that will be formed are outside two. Will it remain even after multiplying or else That means you only need to know its number of factors. How will it come if it is taken out? Add one to the power. 6 + 1 Add one to the power i.e. 4 + 1 equals 35 Multiple has arrived. such option Add one to three And this is 7 to the power of 1. Add one to the forest So 7 * 5 = 35 8 280 this is it. Tell me it's cool Isn't it? Let's move ahead. Are What is recorded I will show you now Let go Let's move ahead. Number of a number Factor, Sum of Factor, Even Factor, Odd I taught him everything about factors, so and so. Big Let's take the number. Suppose this is a number is n. Its prime factorization gives It has happened. 2^11*3 to the power of 7*5. Let's say this is a number n. Us Tell how many factors this number has Are there any that are perfect squares? This How many factors of a number are there such that Are they perfect squares? Did you understand? How many factors does a number have that are perfect? How will you remove it? How many factors does this number have such that are perfect squares. Perfect Square means what should always be the power Needed? Multiple of two. Always Power What Should it be? Multiple of two. So look here But you see three things. 2 of 11 to the power, 3 to the power of 7, and 5 to the power of four. They have to have children who are multiples of two. yes. And one more thing to keep in mind is that the forest One is also a perfect square number. of the forest Square. So just in case you find the perfect one here The factors of this number n have to be found. which are perfect squares. those of the number n The number of factors that are perfect squares. So what do you need to take? here 2 11 3 7 We have to take those children of 5 4 who are even. So 2 11 to the power of 2 will be subtracted from 0. Because What is 2 to the power 0? Forest. One is also perfect Isn't it square? 2 to the power of two 2 four to the 2 power six to the 2 power eight to the 2 2 to the power of 10 not to the power of 12 Because 2 to the power of 11 is itself 3 to the power of seven 3 to the power of seven those children Where the perfect squares are where the power It is even. 3 to the power 0 32 3 Those children of 5 where power is even. Isn't it? So 5 to the power 0 5 to the power 2 5 to the power 4 here comes the. Any problem? The number of combinations that will be formed by multiplying them What will all of them be? perfect Square. Like 2 to the power of 6 to the power of 3 2 and 5 will multiply into 4. how perfect Is it square or not? Tell me, dear children How many factors will there be? How many are these Will there be combinations? 1 2 3 4 5 6 1 2 3 4 and this becomes 1 2 so 6 * 4 = 24 * 3 So that means how many factors does this number have? Are? Perfect squares of this number are 72 Factors Perfect. Any problem? Not there. No? This happened. I explained it to you. But Listen carefully. I have a trick for it Is. What is that you can You can find out directly how much it Factors Perfect. of a perfect square Meaning what power is needed? Power is needed even. Two What multiple do you want Sachin? of two you Look, 2 to the power is 11. The power of 2 is 11. 2 How many times will even appear in the power of 11? Power Divide 11 by two. Two to the power 11 Run away. So 2 * 5 divided by two to the power do it. Divide the power by two. 11 to two Will participate. 2 * 5 will go into five times. Five Add one to it. Did you enjoy it? This is the power of seven. to the power seven Divide by two. 2 * 3 2 * 3 = 6 three Will go to the bar. Add one to it, dear. Children. Isn't it four? The power of five is four. Divide by two. 2 * 2ni will go twice. Add one to it. Look at this combination Are they being made or not? Six 4 and three are visible Are. Is it clear children? Have you arrived? Understand No? Understood? No problem. Ok. Me I think you understand the matter well I am coming. Okay, right? Come on, tell me this. A number is given in front of you. of this number How many factors are perfect squares that Are there more than one? Brother, one is perfect It is a square number, right? So, of this number We have to count the factors which are perfect squares. There are but one bigger one. So brother, first thing So this number So there is no prime factorization. Number What is? 2 to the power of 4 * 3 to the power of 10 What is 10 to the power of? 2 * 5 10 its If we raise 4 to the power then 2 to the power will also be four. And the power of 5 will also be four. So you are the most First fix its prime factorization. So 2 to the power 4 2 to the power 4 2 to the power The power of 3 times 5 is Sachin ji and 5 Power four, no problem now with this number Find the factors that are perfect Find the factors of this number which is a perfect square. Perfect Square Told the trick to remove it. to the power of two Multiply it. +1 8 / 2 4 + 1 5 to the power multiplied by two divided by two do it. Five divided by two twice Will go. 2 + 1 three multiplied by four by two If we divide it, it will go twice. two and one 3 * 3 = 9 * 5 i.e. the total of this number There are 45 factors that make a perfect Of the 45 factors that are perfect squares There will also be a factor one because one also If you have a perfect square number, you don't get one. One will have to be reduced to one, which means 44 remain. Factors that are perfect squares of the number of options Did you come and enjoy it? Come on my brother tell me this CHSL It is a question of 24. I will also see who will do it. This. We Excellent. How many factors of this number are 120? Are there multiples? Isn't it? How many of this number Factor multiples of 120? Isn't it? that's it Have to take it out. Tell me, dear children. How many? Factor? CHSL 204 As It Is question Is. Asked from previous year. you won't do it So what should we do? So brother, what do you do about it first? do it? Fix prime factorization. Isn't it? 2 to the power of 8 * 3 to the power of 6 times 2 to the power of 8 6 * Power of 5 4 * 10 to the power 10 means 2 * 5 = 10 so 2 to the power of 5 * 5 power so you can see that 2 to the power is 8 And 2 to the power 5 to the power of 2 totals 13. 5 4 to the power of 5 to the power of 5 so 2 to the power 13 and power of 5 Your mind should work fast, dear children. 2 of power 13 5 to the power 9 this prime Factorization arrived. Have you come? this is normal The thing is. anyone can. Now we need The factor which is a multiple of 120. So in this Pull out 120 from it. 120 what It happens? 15 * 8 = 100 i.e. cube of 2 8 * 3 = 15 and not 2 cubed by 8 * 3 = 24 * 5 = 100 here we go brother, we got that factor If it is multiple of 120 then 120 Pull out the cube of 2 = 8 * 3 24 24 * 5 = 100 Now if we take this out If we take it one way, what will be left inside? 2 to the power was 13, so what remains is 2 to the power of 3. three to the power of 6 taken away from three to the power of 5 five to the power of 9 This is it, so we only need this product. factors have to be taken out because they are all What if all the factors outside are multiplied by 120? will be Isn't it multiplied by 120 and everything is 120? Multiples will be just its factor count So 10 + 1 5 + 1 and 8 + 1 then 11 99 99 sixes are 6 less than 600, which is 594. 594 options Number Is it okay kids? You can also do this That you first divide it by 120. Whatever goods remain after dividing, Factors have to be found. You can do that too, right? It's the same thing. What should you do first? This Divide it by 120. Okay, right? But he I won't tell. Let us tell you this. This is the best question ever. What is this? Are? Railway NTPC Govind ji you have a lot of mathematics Comes. Please break this question down. So it will be four 20 40 40 It will be 40 only Let's take a look cube of 2 cube of 3 cube of 5 power of 4 * 7 Square These Already Prime Factorization Is. It will not break further. How many of this Factors that are divisible by 50 Yes, but not 100%. do you understand what I am saying In? What am I saying? big cheese Is. How many factors of this number are there such that 50 is deductible but not 100 is deductible Cut. Like these ones 50, 150, 250, 350 I have to tell its factors. Is it okay, kids? Just think. So brother, first you take out 50 from this. We need a factor that is divisible by 50. Is. That is, those factors of this number We have to find the number which is a multiple of 50. Are. So first you take out 50 from this Take. What is 50? 25 * 2 = 25 * 2 = How many factors of this number 50 are there which are divisible by 50? Is it divisible by? Divisible by 50 means 50 Multiple of. So take 50 out of it. Take. So what will be left, dear children? Tell me. The power of 2 was three. Two to the power of two will remain. 3 to the power of three remains. 2 to the power of 4 Removed. 5 to the power of 2 * 7 to the power of 2 Will come. This is what will come. Okay, right? So you will see that What did I multiply this by? I am multiplying all this data by 50. So whatever number of factors it will form What will all those be? 50's Multiple of 50 But remove those which are multiples of 100. They are made. What does 100 mean? 50 double 50 doubles to 100 As soon as this 50 is put inside What will happen if two people come together? 100 It will become 100, right? As soon as this 50 is in What will happen if we get the support of these two? That means this 50 is supported by the two inside. Don't give it to me. Don't take this. Don't give this. So, this 50 if this one If you multiply the data, then all of them What will be the factors? 50's Multiple Butts Not multiple of 100. So, only whose Do you want to find the factors? Did you enjoy it? Did you enjoy it? I know how you are like that He is a child. The bastard would not have been happy. Anything They have it in their mouth. Add one to the power. 3 + 1 4 2 + 1 three 2 + 1 three so 3 * 3 = 9 4 what is the answer Is? Option Tell me children, did you enjoy it? Let us give you motivation. Saw this I was called to the studio by some South Indian people. He is a Maitri movie maker, right? Who made Pushpa. They Called to do your screen test. He did my photo shoot. Excellent Also wore glasses. Then I took up acting. But I started teaching. I gave a tough fight to Saurabh Dwivedi. He said cancel. Then I used this photo and got motivation Wrote the line. Got back to my work. If you find it difficult to study today, then tomorrow It will be even more difficult to regret. If you read it today If you are not going then it means your time is being wasted. Used to be. It was the age to study. not even reading If you don't study, you won't get a job. and when If you don't get a job after 510 years, you will earn less money. will be. If there is nothing to spend, then What will happen? regret Study today and get a job. regretfully yesterday You will get salvation. Got it? Are they crying or living? what to say Are these there? Are laughing. laughing emoji It is about to happen. Let go Come. Let's move on, dear brother. Have these questions for CHSL 2024 Pre? Is. This is the best question. Tell me this question What is the answer? Now change the type from here Went. What happened? Type change. same I will ask this type of question. Tell. Hey wake up everyone wake up everyone there is water in the bed Pick it up one by one, everyone's father-in-law should not come studying. Yes, it's 1:00 am, they're sleeping, they're bastards. You should read it at this time Yes Tell me it's 1:00 in the night and he's sleeping. It's time to study. Yes. A natural number n divides 732. and gives remainder 12. How many values ​​of n are possible? Are? Govind ji? A natural number divides n 732 Leaves 12s reminder. How Many Values Of n are possible? is a natural number n i.e. that positive integer. when 732 is divided by n If you do this, a reminder comes 12. of 732 Meaning 720 + 12. I can write my Brother. So when I multiply this number by 732 Is. This is the number I get when I divide by n. then the remainder on dividing is only 12 comes. What is the remainder? That means where did 720 go? This is 720 complete The whole is cut off from n. 720 whole to n The exact division happened. That is, the number n Whatever happens, what will it be? one of 720 Will be a factor. Will it happen or not? That means that The number n is a factor of 700 20 Isn't that it, kids? No problem Heman Khede ji, you must have understood this correctly, right? 720 divided by n 732 divided by n If the remainder is 12 then it means 720 + 12 I can write 12 remainder left 720 subtracted from the number n, that is, the number is a multiple of these 720 Will be a factor. This is what is asked for how many values ​​of n Is it possible? As many factors as there are of 720 Only these values ​​of n are possible. But there is a flaw. If 720 is divided by n, the remainder is 12. If the value of number n is greater than 12 then will be. On dividing a number The reminder is always smaller than the divisor. If the remainder on division by n is 12 So the value of number n is greater than 12. It must be so. Divide by a number greater than 12 Only then can the remainder be 12. Then the value of n What should happen? Greater than 12. and the value of n There should be a factor of 720. So how many factors of 720 are there which are divisible by 12? Are you big? So first factor the total of 720 Take it out. Govind ji, factor of 720 means What does 720 mean? 720 144 * 5 144 * 5 = 720 144 means 16 less 16 less 2 4 to the power of 16 = 3 squared 9 16 * 9 144 * 5 = 700 20 is easy work. numbers Build a relationship with. So tell me the total of 720 What are the number of factors? How many are there? Add one to four and you get five. Two I will add one to Three. If you add one to one then 5 * 3 = 15 * 2 ni to total here 720 30 is the only factor. Any problem? But 30 There is no answer. The total factors of 720 are 30. We need the factor that is divisible by 12 to 720. What factors are smaller than 12? one 720 one is divided by. Even from two, even from three, Even from four, even from five, even from six, even from eight also, also from 10 and also from 12 and sorry from nine Too. Isn't it? than nine and so these 720 are factors that are greater than 12 are smaller than or equal to 12. Isn't it? So How many are these? 1 2 3 4 5 6 7 8 9 10 10 so There are a total of 30 factors of 720. but in that There are 10 factors whose value is less than or equal to 12. So we Don't take this 10. So 720 then 20 Factors remaining that are 20 from 12 to 720 Increase by the factor 12 and that is the value of n It may be possible. So what is the answer? Isn't this an amazing question? Enjoyed it and let's move on. Let's go and tell you the next concept So, what do I do Let's take the next concept in front of you. Let's tell you the last concept, dear children. The last concept and on this concept this year The question came in the Mains paper. did you come or not Govind ji? Square of any prime number There are exactly three factors. You have whichever Square the prime number. His There will be exactly three factors. Not less than three, Not more than three. Write it down. any Exact Three of the Square of a Prime Number There are factors. Not less than three, not more than three From. Suppose 11 is a prime number. Is. How is 11? Prime number means prime Numbers that are divided by one and divided by themselves and by any other number Don't cut it. So like prime number I For example, take 11. Square of 11 What happens? The square of 11 is 121. So what is 121? of prime numbers So 121 is either divisible by 1 or divisible by 11. Or it will be deducted from 121. There will be only three factors. The fourth one won't be made, right? So because of this Dear children, the value of any prime number Let p be a prime number. Let's assume p is any prime number. p is any prime Number. So if you multiply a prime number by We will square it, that is, the square of p. So it will either be cut off from one or from p or p² From. So there will be only three factors of a prime. Square of the number. Okay kids? Now let's look at the question on this, dear friends. This question came in CGL Mains 2025. How many such in the set 1 2 3 dot dot 100 What are integers whose exact divisor is three? Divisor or factor is the same thing. from one How many numbers are there up to 100 which have Exact There are three factors? from one to 100 It has just begun. So are you unable to sleep? How many such numbers are there from one to 100? are integers whose exact three divisors Yes, there are three factors? Look at any prime Exact three factors of the square of a number There are. So from one to 100, that Looking for numbers that are multiples of a prime number Squares are formed. Isn't it? So like the forest It is not prime. So the square of two is Four dear children will go. only three out of four will be a factor. One, two, and what comes next? Three is a prime number. The square of three is nine. There will be only three factors. One, three and nine. Then Will he come? Square of five. will come again Square of seven. will come again Square of 11. 121 which goes beyond 100 Will go. That means you only need these four. The numbers will appear. In the range of one to 100. Square of prime number whose exactly three