first of all thanks for being here in my youtube channel so in this lesson number four on the topic number system now we are going to learn a concept called a reminder theorem so reminder theorem is nothing but to find a reminder of the number usually they will give some sort of question for example 23 power 5 divided by 5 so we have to solve the question we have to divide the numbers and we have to find the reminder for it right so those type of questions we are going to learn in this lesson number four so listen here friends lesson number three that is previous lesson is most important lesson finding a unit digit got it so this reminder theorem is a rare case right in the exams most of the competitive exams usually they will concentrate on the previous lesson unit digit but if you are preparing for cat exams or else a gate exams or else ssc exams those students should concentrate on this reminder theorem also so friends listen here this reminder theorem is subdivided into two categories one is finding a reminder for the normal numbers got it so normal numbers let me take 23 by 5. so they usually give a question like this and our target is to find what is the reminder got it it's a normal numbers and the second will be a polynomial numbers polynomial numbers is nothing but for example x square plus 7 x plus 2 so this complete term should be divided by x square plus 2. so we have to find what is the reminder for this number so listen here if you are preparing for cat gate exams then preparing for any campus interview so those students should concentrate both the topics right you need to concentrate both the sections because in most of the cat exams they have asked a question from this area and most of the gate exams they have asked a question from this area the sse also got it so you have to concentrate both but if you are preparing for any state level competitive exams for example tamilnadu state level or big or state level competitive exams gujarat state level etc you have to concentrate 80 percentage on this topic and 20 percentage on this topic so got it so based on the exams what you are preparing you need to concentrate on this reminder theorem right so here in this video i am just going to teach you the normal numbers how to find the reminder for the normal numbers so in the next video i will be teaching how to find the reminder for the polynomial numbers right so friends listen here in this video we are going to solve 10 question that is based on a normal numbers first and foremost is by seeing a question don't decide the question is tougher for example the question will be given like this 517 power 5 17 divided by 5 just see here if you see the question like this 5 17 power 5 17 we have to find the reminder for this question right by seeing the question don't decide the question is difficult again i am saying there are very simple logics to solve this question very easy it requires some practice if you practice those questions then solving all the tough level question based on this normal numbers will be easy but before that you have to buy out some of the numbers 2 power 1 is 2 2 square is 4 2 power 3 is 8 so till try to learn up to 2 power 5 got it so similarly 3 power 1 is 3 3 power 2 is 9 so similarly try to learn up to 3 power 5 it is enough these two numbers are more than enough to crack the question got reference so let me want to all the questions that is based on a normal numbers so initially let me go with five example questions right so first question 23 by 5 so we have to find what is the reminder for 23 by 5 so usually how will you find the reminder you will divide 23 by 5 times so no five fours are 20 so what about the reminder here three so we would say the answer for this question is three so the reminder is three every time in the exams you should not do like this it's completely waste of time right for those cases what you need to do is you try to directly cancel year itself in the mind calculations and try to find the reminder just see here how many times 5 into 4 is what 20 so what is the reminder that we have what is a balance number if 5 into 4 is 20 what will be the balance number is 3 so we call 3 as a reminder got it or not right always try to find the reminder for all these types of numbers in the mind calculation do not do like this it's a schooling method you should not proceed in this way to solve all these questions right so let me take the second example 17 divided by six so what is the reminder six threes are 18 but six twos are 12 yes or no 6 into 2 times is what 12 so what is the reminder that we have is 5 so 5 will be the reminder for this question so friends got it or not right so 6 into 2 is 12 so 17 minus 12 is 5 so reminder is 5. so one important note never forget this note right so never and ever forget this note while solving the reminder theorem always after finding the reminder you have to check the reminder number the answer that we got reminder should be low when compared to this denominator number see for the first equation the reminder is 3 the denominator is 5 always the reminder value should be low when compared to the denominator value similarly here we got the reminder 5 so the number 5 is low when compared to 6 so we are saying that the reminder will be 5 got it so let me move on to the third question just a third question 86 into 23 divided by 11. so friends just listen here you don't want to multiply like some students what they usually do is they will multiply 86 into 20 then they would find the answer and then finally they would divide by 11. don't do that it's a time waste what you need to do here is you need to divide all the individual numbers by 11. first divide 86 alone by 11 got it so how many times 8 times will be 88 7 times will be 77 yes or no 11 into 7 will be 77 got it so what is the reminder that we have if it is 77 6 7 8 9 so 9 will be the reminder got it or not again divide 23 by 11 2 times 11 into 2 is 22 so we got a reminder as 1 so finally 9 into 1 will be 9 so 9 is the reminder for the given number so friends understood or not how i am solving it right so you have to divide each and every number individually by 11. you don't want to multiply both the numbers it's a completely time waste i am just dividing 86 by 11 separately 23 by 11 separately after finding the reminder i am multiplying both understood or not right so let me move on to question number four 38 plus 71 plus 86 listen here so first first you can either you can add all the numbers and then you can divide by 16 you will get the answer or else what you can do is you can divide all the individual numbers by 16 first divide 38 by 16 1 16 are 16 16 2's are 32 16 3's are 48 but our target is 38 right so we can say that 16 into 2 will be 32 so 30 to 38 what is the reminder we have 6 is the reminder got it so similarly 16 into 4 will be 64. so what is the reminder that we have is 7 got it so similarly 86 divided by 16 16 fourths are 64. 16 5's are 80. so what is the reminder that we have a 6 got it so finally i am dividing all the individual numbers by 16 38 by 16 71 by 16 86 by 16 and finally i got all the reminders here first let me add the reminder 6 into 6 sorry 6 plus 6 will be 12 12 7 will be 19 you should not say 19 is the reminder why because just now i have told you keep that in mind never forget this note always after finding the reminder you have to check the reminder should be low when compared to the divisor that is by dividing the number right what we are going to divide see 19 is not low 19 is the highest number when compared to the divider right what you need to do is you need to again divide by 16 if you divide by 16 1 16 are 16 reminder will be 3 so finally the reminder for the question is 3 friends understood or not right always remember that after finding the answer you need to check whether the reminder number is low when compared to the divisor got it if it is not low then you have to again divide by the divisor so divided by 16 so one times a reminder will be 3 so finally 3 is the reminder got it now the reminder value is low when compared to the divisor so this is the way you have to solve the question so fifth question 123 into 124 into 125. see multiplying if you start multiplying all the three numbers how much lengthy it is first you need to multiply 123 into 124 after finding that answer you have to again multiply by 125 so don't do that what should be a target you need to find what is the reminder for all the numbers individually so divide 123 by 9 right if you divide by 9 1 9's are nine so reminding us what three thirty three nine threes are 27 so reminder is what six so finally we can say that six will be the reminder for the first number for the second number seven will be the reminder for the third number eight will be the remainder got it because 123 6 then 124 will be 7 125 will be 8. so totally the reminders are 6 into 7 into 8 divided by now what you need to do is you can multiply 6 into 7 so 6 into 7 is 42 so 42 into 8 by 9 got it so again for the individual numbers divided by 9 if you divide 42 by 9 so nine fours are 36 so reminder will be six here so this will be the reminder so again we got six into eight divided by nine so eight six are 48 by nine got it so 9 into 5 will be 45 so remaining will be 3 got it so finally we can say that answer for question number 5 is 3 so friends understood what i did so for every number individual numbers i am just finding the reminder reminder at last i'm fine finding the final reminder always remember that the final reminder value should be low when compared to the divisor right right so initially i found the reminder for 123 6. if you divide 123 by 9 reminder will be 6 similarly for the next number is 7 for the last number is 8 and then we have to multiply all the numbers so 6 initially i have first multiplied the 2 numbers 6 into 7 is 42 so 42 remaining number is 8 divided by 9 again for the individual number 42 i have divided by 9 so reminder will be 6 so 6 into 8 again 16 into 8 is 48 right so 48 divided by 9 9 5's are 45 so reminder will be 3 so 3 divided by 9. so finally we can say that we got a reminder 3 further you don't want to divide by 9 why because 3 cannot be divided by 9 9 but can be divided by 3 but 3 cannot be divided by 9 so finally we can say that reminder for question number 5 is 3 question number 6 so 7 power 5 divided by 4 so we have to find what is the reminder for this number see here if it is 7 square by 4 it is easy to find the answer because 7 square is 49 if it is 7 cube 343 by 4 that is also easy but 7 power 5 finding a number for 7 power 5 is very much difficult so what you can do here is you can write this 7 power 5 as 7 into 7 into 7 into 7 got it divided by 4 got the logic or not now every individual number i am going to divide by 4 if you divide 7 by 4 one fours are 4 reminding us what 3 so for every number we got a reminder 3 3 3 and 3 friends got it or not so 3 into 3 into 3 into 3 into 3 divided by 4 according what i did so for every individual numbers for every individual number i am dividing by 4. if you divide 7 by 4 one force or 4 reminder will be three so that's the thing i have written here right for first seven reminder three three three now what i can do here is i can multiply the first two numbers three into three is nine again three into three is nine got it so by four got the logic or not again i'm going to divide the individual number by four so how many times four twos are is what eight what is the reminder here one again four twos are eight reminder is one so one into 1 into 3 will be 3 so finally we can say that the reminder for 7 power 5 divided by 4 is 3 you don't want to divide 3 by 4 just now i have told you you need to find the reminder but remember one thing the reminder value should be low when compared to the denominator number never forget this right sometimes students will make a mistake that's that's the thing i'm repeatedly saying this always remember that after finding the reminder check one time with the divisor always the reminder value should be low when compared to the denominator number that is the division got it so finally we can say that three will be the reminder for question number six so friends got it or not right i'm just finding the reminder reminder reminder till i get the last reminder got it so this will be the answer for question number six so question number seven so 2 power 75 divided by 5 so now we are entering into some difficult level question just here if it is 2 power 5 example i am saying if it is 2 power 5 it is easy to write 2 into 2 into 2 into 2 but here the number is 2 power 75 we can't able to write like that right so what you need to do is just now i have told you initial stage of the video you have to buy out some of the numbers 2 power 1 is 2 2 square is 4 2 cube is 8 so after biting all the numbers just listen carefully what i am going to do is i'm just going to uh just see i can write here 2 power 1 is what 2 square is 4 2 cube is 8 2 power 4 is 16 this year 5 under 16 i can mult 5 into 3 is what 15 right so this 16 number right the number 16 is most probably nearer to this 5 multiples yes so now 5 into 3 is 15 so 2 power 4 is 16 now i'm just going to convert the numerator value as just listen carefully 2 power 4 got it 2 power 4 right so divide this 75 by 4 if i divide 75 by 4 so one fours are 4 so reminding us three right 35 so 35 is eight fours are 32 right so remaining is what three so this can be written as two power three divided by five so friends try to understand how i wrote this so if you understood this logic then solving all the questions will be easy got it how i write this initially they have given a number as 2 power 75 right by seeing a denominator number is 5 we already learned up to 2 power 5 in the initial stage of the video right so you have to check 5 multiples which number here right you can take 5 multiples of 16 why because it is little bit nearer number 5 into 3 is 15 so i can take 16 here nearer number so i am just going to convert this 2 power 75 as 2 power 4 because 2 power 4 is 16 so 2 power 4 power 18 into 2 power 3 so 18 into 4 2 power 3 if you add both the numbers you will get 2 power 75 now what i can do is this 2 power 4 can be written as 16 power 18 into 2 cube will be 8 divided by 5 got it because 2 power 4 is 16 right so power 18 asset is 2 cube is 8. now just here for individual number this individual number alone i am going to divide by 5. so 1 5's are 5 phi 3s are what 15 reminder is what 1 so 1 power 18 into 8 divided by 5 understood or not right what i did 16 power 18 got it for this individual number 16 alone i'm going to divide by 5 16 by 5 will be 3 times 5 into 3 is 15 so reminder is what 1 so 1 power 18 into 8 by 5 1 power 18 so 1 power any number will be always 1 so this can be written as 8 divided by 5 you should not stop here why because i have just told you the remainder value should be low when compared to the divisor so again 1 5s are 5 so reminding us what 3 so 3 will be the reminder for this question so friends understood or not how i did this if you can't able to understand it again start watching from the first stage of the video and for complete uh solving this question this step alone is important by just watching one question you can't able to understand it it requires more practice again i am saying take your books practice 10 or 20 questions automatically you know how to write like that got it so first 2 power 4 is 16 right some students will ask why i can't able to take 2 power 8 can i take 2 power 3 yes you can you will get the same answer but always remember that try to take the divisor nearby multiples only then it is easy to solve the question so 5 3 will be 15 so only i have take 2 power 4 right so 2 power 4 i have just divided 75 by 4 is 18 remainder is 3 got it so i have written as 18 here the reminder 3 has 2 power 3. so now if you add 18 into 4 and then 2 power 3 you will get 75 okay so finally answer for question number 7 where the reminder is 3 question number 8 so just see the question number 8 7 power 129 divided by 5 so we have to find the remainder so from just here 7 power 129 it is not easy to write 7 into 7 into 7 so we have to use certain tricks to solve this question just listen carefully first what i can do is in the previous question the numerator is 2 so we can easily write down as 2 power 4 something but here the numerator is 7 so what you need to do is just take the number 7 alone just listen carefully just take the number 7 alone right not the power 129 i am just taking the number 7 alone 7 individual number divided by 5 so 1 5's are 5 reminding us what 2 so the remainder is 2 so 2 power 129 2 power 129 divided by 5 so friends understood this step or not how i wrote this i am just dividing the individual number 7 alone by 5 7 by 5 1 5 5 the remainder will be 2 so now i write this complete number as 2 power 1 29 by 5 right so 2 power 129 by 5 now it is easy to convert the numbers because just now we have learned 2 power 4 is what 16 nearby multiples got it two power four so divide completely by four so four threes are twelve so four twos are eight so reminder will be one so this can be written as thirty two got it reminder one can be written as two power one by five that's it now it is easy or not how i wrote this initially i have found the reminder for 7 by 5 that is 2 so 2 power 129 by 5 just now we have learnt we have to check the 5 multiples 5 3's are 15 so we can write the numerator 2 power 4 as 16 so 2 power 4 right divide 129 by 4 so it is 32 reminder 1 i am writing as 2 power 1 if we got reminder 2 2 power 2 if we got reminder 9 2 power 9 got it or not right so now we can say 2 power 4 is what 16 so 16 power 32 into 2 divided by 5 so now cancel it 1 5's are 5 how many table how many times 5 3 is a 15 reminder is what 1 1 power 32 is always 1 so the complete for this number the reminder will be 1 so this can written as so finally we have only number 2 so this will be the reminder because the number 2 is low when compared to the divisor so we can say that 2 will be the reminder how easy it is first question alone previous question alone it will be little bit difficult but see how easily we have solved this question so only important area is this area got it and then you have to understood this concept you have to understand this concept right just see here 16 power 32 we can cancel it 5 3s are 15 so what about the reminder will be 1 is the reminder 1 power 32 so 1 power anything will always be 1 so 1 into 2 will be 2 you don't want to divide by 5 why because we got a reminder which is low very less number when compared to the divisor so definitely 2 will be the reminder for question number eight question number nine so question number nine is 517 power 517 divided by five just see here by seeing the question again this is according to me it's very small question the exams they usually ask 517 power 517 into 2300 etc so by seeing the question do not decide it is difficult it is always easy if you know the logic what is the first step you have to do you have to divide this individual number 5 17 alone by 5 let me divide this 1 5s are 5 right 0 phi 3s are 15. what about the reminder that we have is 2. so totally we got a reminder that is 2 5 17 by 5 understood or not how i wrote this i am just dividing this individual number 5 17 by 5 if i divide 5 17 by 5 we got a reminder 2 so this complete number we can write this as 2 power 5 17 divided by 5 now just look at the denominator what about the denominator here 5 so the numerator is 2 convert in terms of 5 multiples so you can write this as what 2 power 4 just now i have told you 2 power 4 is 16 multiplied by multiples of 5 right so divide by 4 so what about the one force of 4 right so remaining will be 1 again four twos are eight so remaining will be three that is thirty seven eight fours are nine fours are 36 remainder will be one so 129 so reminder we got to 1 that is 2 power 1 by 5 understood or not right i am dividing 5 17 by 4 we got 129 and the remainder 1. so i have written 129 here and reminder as 2 power 1 quarter so now we know the 2 power 16 2 power 4 is 16 when you cancel 5 and 16 remainder will be 1 so 1 power 129 always it will be 1 so finally we got 1 into 2 by 5 so 1 into 2 will be 2 so 2 will be the reminder quad it or not see how easy it is the question looks little bit uh by by seeing the question we we feel that it's difficult but just see here how easy it is it comes only in practice right so answer for question number nine where the reminder is two so last 10th question so what is the reminder when 2 2 4 3 power 165 2 2 4 3 power 165 is divided by 4 usually in the exams they will ask question like this so we need to write like this and then we have to find the reminder just see here 2 2 4 3 power 165 divided by 5 so our target is to find what is the reminder so what what is the first step you need to do you have to divide this individual number alone by five let me divide this five fours are what 20 so reminder is 24 again five fours are 20 reminder is 443 eight fives are 40 remainder will be 3 so this can be written as 3 power 165 divided by got it or not and all the previous question we got the reminder two but in this question we got a reminder three don't worry about it sometimes you will get a reminder four or reminder eight whatever be you have to write reminder three power one 165 the next step just listen here just now i have told you right you need to check the nearby multiples of 5 only then you can convert the number just here what is 3 power 1 3 power 1 is 3 3 square is what 9 got it it's not nearer to the multiples of 5 got it so 3 part 3 is 27 again not the nearby multiples 3 power 4 is what 81 yes or no 3 power 4 is 81 got it which is a nearby multiples of 5 because 16 into 5 will be 80 so here you can see 3 power 4 is 81 so we can take 3 power 4 so now i am going to convert this as 3 power 4 so divide this by 4 if you divide by 4 it is 41 so reminder will be 1 so 3 power 1 by 5 got it or not how i wrote this so 3 power 4 if you divide 165 by 4 we got 41 and reminder 1 i have written 41 here and the remainder 1 year so now we need to divide by 5 just listen here 3 power 4 is what 81 yes or no so 81 power 41 into 3 divided by 5 so if you cancel 81 by 5 right 16 5s are 80. so reminder is 1 1 power 41 anything just now i have told you one power any number will be always one so for this complete number the remainder will be 1 so 1 into 3 will be 3. so finally answer for this question where the reminder is 3 just see every question have a certain logics if you use that logic solving a question is easy i have told you the logic first unit what you need to do you have to divide the individual number by the divisor right either not every time it won't be five sometimes it won't be six or seven or eight whatever b but you have to divide by that number and you need to find the reminder after finding the reminder you have to check the nearby multiples of the divisor so here i have taken 3 power 4 why because 3 power 4 is 81 where 16 into 5 is 80 so 80 81 is a nearer number so i have taken 3 power 4 divided by 4 41 and reminder 1 so just now i have told you 3 power 4 is 81 if you divide 81 by 5 reminder will be 1 1 power any number will always be 1. so for this complete number the reminder is 1 and the remaining number that we have is 3 power 1 is 3 so finally we can say that the reminder is 3 so hence that's it about this video so again i just want to say one thing listen here it requires a lot a lot of practice just by watching this video you can't able to solve the question in the exams you have to take your books after watching video after understanding the concepts take your books or search in a google you will get more than 100 200 questions try to solve all the questions right so some students will solve in a minus terms for example they usually write like this minus 3 per 4 right in most of the foreign other books or a local author books you can able to see my they usually convert in some numbers they convert in terms of minus it is not required right either you convert into minus you are going to get the same answer if you convert into a positive value you are going to say get the same answer always try to learn any one method right don't learn both the methods both the methods will be confusing that's the reason i have converted all the numbers in terms of positive value right got it so just some students will ask me this doubt some books they have written in terms of minus so don't get confused all the questions use the same logic you will surely get the answer so thank you so much for watching this video so if you really like it share the video to your friends those are preparing for the competitive exams so thank you so much for watching it bye