# PLAYING WITH NUMBERS| CHAPTER 3| EX 3.5| GRADE 6| INSIGHTFUL MATHS

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PLAYING WITH NUMBERS| CHAPTER 3| EX 3.5| GRADE 6| INSIGHTFUL MATHS

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00:00Hi everyone, welcome to insightful maths. Today's session is about prime factorization.

00:06We will be doing this topic using exercise 3.5 playing with numbers grade 6.

00:13Before starting the session, if you have not liked and subscribed to my channel, please like and subscribe.

00:20So the session starts with the first topic which is prime factorization.

00:27In prime factorization, what we do? Any number should be written as the product of its prime factors.

00:35Now what does it mean? If I have a number 12, so I can write this number 12 as 2 multiplied by 6.

00:43But 2 is a prime number, 6 is not. It's a composite number. So this is not the prime factorization.

00:51So how I am going to do it? Start the repeated division of this number 12.

00:57We can do this directly as well or otherwise if you feel this method useful, you can do it in this manner.

01:032 x 6 is 12, 2 x 3 is 6 and 3 x 1 is 3. Right? We have done the repeated division.

01:14Please ensure one thing that we never include this 1 in the prime factorization.

01:20Why is that so? Because 1 is not a prime number. So we have to write this 12 as the product of 2 x 2 x 3.

01:32This is the prime factorization of 12. Let's do one more example.

01:37If we have the number 36, you can see here prime factorizations are being done.

01:43I am doing the repeated division for you to understand how you have to prime factorize any given numbers.

01:50Now 36 being a prime number, it is divisible by 2. So 36 x 2, that's 18.

01:5818 x 2 is 9, 9 x 3 is 3 and 3 x 3 is 1. We are not going to include this 1 as it's not a prime number.

02:12So out of the given options, which is the correct answer for prime factorization?

02:17Have a look. These all products will give you 36. But 18 is composite, 12, 9, 4.

02:27These are the composite numbers. So it is not a prime factorization.

02:31So this is the correct answer. Have a look. 2, 2, 3 and 3.

02:37So you have to write the final answer like this. 36 is the product of 2, 2, 3 and 3.

02:46That's the answer for prime factorization.

02:49Moving on to the next topic. Making a factor tree of the given number.

02:55Please understand if I have a number A. Okay, any random number.

03:00If I am branching this number, so the product of these two numbers should give you A.

03:07What does that mean? If I am making the factor tree, let's say of number 36.

03:13Advisable, break it in such a manner that at least one number should be the prime number.

03:19So I know that this is an even number. So 1 prime number 2.

03:24Let us circle every time we are getting the prime number.

03:28It will make your task easier when you write your final answer.

03:31So 2 into which number gives you 36? That is 18. We'll write 18 here.

03:38Once again, 18 can be broken in two parts. One number, even number 2, prime number I am again taking.

03:472 into 9 is 18. 9 is composite here, which can again be broken as 3 multiplied by 3.

03:56Now how many factors have we got? 1, 2, 3, 4. Is it not looking like a tree?

04:02It's looking like a tree. That's why the name here given is factor tree method.

04:08So again, we have bought the matrix of 36 as this one 2.

04:13Again, one more 2. Then we got 3 and 3. That's your final answer using factor tree method.

04:23So after this, these are the basic topics we'll be using in this particular exercise.

04:28You will be understanding it better once we are going to do the textbook questions.

04:33So starting with question number 1 of exercise 3.5, we have the starting number as 60.

04:40It is split in two parts. Check once again. 6 into 10. It is giving you 60. Easy enough.

04:47Now the product of which two numbers will give you 6? 2 multiplied by 3 gives you 6. That's the answer.

04:55We have the number 10 here. 5 multiplied by which number is 10? That is 2. Answer is 2 here. Good to go.

05:05Alright. Now 60 is divided in two parts. 30 multiplied by this number should give you 60.

05:1430 multiplied by which number is 60? That is 2. Answer is 2 here. Likewise, 10 multiplied by 3. It's 30.

05:25Now split 10 in two parts. Which two numbers multiplied will give me 10?

05:30It would be 1 into 10 also, but we are taking the prime numbers. So that is 2 multiplied by 5.

05:38Your answer is now 2, 5. The product is 10. I hope this much is easy enough. Let's move to another question.

05:46Now question number 2 is easy enough that I have just repeated.

05:50Which factors are not included in the prime factorization of a composite number?

05:56For example, I have a composite number 4. Can I write it like, if I repeatedly divide 2 into 2 is 4, 2 into 1 is 2.

06:06But 1 is also the factor. But do we include this 1 here? I do not include 1 ever in the prime factorization as it's not a prime number.

06:17So answer here is 1. Which factors are not included? We never include 1. Reason being, it's not a prime number.

06:28Let's start question number 3. It says, write the greatest 4-digit number and express it in the terms of prime factors.

06:36So it is just like, you know, I mean directly saying do the prime factorization of this number.

06:42The knowledge check is there if you know which is the greatest 4-digit number.

06:47We know this already. Greatest 4-digit number is 9, 9, 9 and 9.

06:53Okay. We have to prime factorize this number as required in the question.

06:58It's your choice if you do through the repeated division of factor tree.

07:02I suggest, unless and until it is not written factor tree, avoid doing that. It's an easy method doing the repeated division.

07:11Okay. Since it's an odd number, we cannot divide it by 2. I'm starting dividing it by 3.

07:189 divided by 3, every time we'll get 3, 3. Now all these numbers are once again divisible by 3. We get 1 everywhere.

07:28Now this number, divisibility rules are going to help you a lot here.

07:34I have made a separate video on divisibility rule. Everyone should go and watch that video.

07:39You'll get a command if this number is divisible by which number.

07:43Now have a look here. 1, 1, 1, 1. It is divisible by 11.

07:49Do not make an error. Generally students do. They give the answer 11. 11 into 1, 11, 1, 11. Have a look.

07:5711 into 1 is 11. Difference is 0 and this 1 will go down.

08:04After taking the difference and bringing the digit down, I have to divide this number by 11.

08:10But it is not divisible. I need one more digit. Whenever you need to borrow one more digit, you need to put a 0 here.

08:19Now easily you can borrow another digit. Right? So 11 into 1 is 11 and it's done.

08:28So we have divided by 11. My number is 101. 101 is itself a prime number. Into 1 and it's done.

08:37How do I know it comes through practice only? I hope everyone is aware between 1 and 100, there are only 25 prime numbers.

08:46So please go and learn those prime numbers. 101 is again a prime number.

08:51So answer of question number 3, how will we write answer of 3? 9, 9, 9, 9.

08:58That is equal to, now write the product of these factors. 3, 3, 11 and 101.

09:07So we have done the prime factorization of the greatest 4 digit number and have a look here.

09:13All these factors are prime factors. Easy enough?

09:18Let's move to question number 4. Exactly a similar question. Now we have to take the smallest 5 digit number.

09:26How do we pick the smallest 5 digit number? Greatest is easy. Every digit will be 8.

09:33When you are taking the smallest number, starting digit has to be 1, rest digit 0.

09:41I have to make a 5 digit number. First digit is 1, rest 1, 2, 3, 4. All are 0.

09:48This is the smallest 5 digit number. Question number 4 we are doing.

09:53Again it has to be written as the product of its prime factorization. So prime factorization has to be done.

10:00It's an even number. So we can start dividing by 2.

10:05I request stop the video, do it yourself and then recheck the question.

10:102 into 5 is 10. All 3 zeros. Now 5000 divided by 2 is 2500. 2500 divided by 2 is 1250.

10:23Again divided by 2 is 625. Now this number is divisible by 5.

10:315 into 1 is 5. 2 into 10 is 5. Again divided by 5 is 25. 25 divided by 5 is 5. Again divided by 5 is 1.

10:44We are not going to take this 1 as it's not a prime number.

10:48How many times 2 is repeated? 4 times. And 5 is also repeated 4 times.

10:55So how will you write your answer? You have to write it in this format.

11:0010000, the smallest 5 digit number is equal to 1, 2, 3, 4.

11:07We have taken 2 4 times and there should be a multiplication sign in between.

11:12Another 5 is repeated 4 times. 1, 2, 3 and 4. So that's your answer.

11:20It is the prime factorization of smallest 5 digit number.

11:25Move to question number 5. It says write all the prime factors of 1729.

11:33Again a prime factorization based question. And you have to arrange the factors in the ascending order.

11:40I request read the question carefully. You'll get to know what all things are being asked.

11:46Step number 1, prime factorization. All the numbers should be prime of course.

11:51Arrange them in the ascending order. Then see if there is any relationship between two consecutive prime numbers.

11:59Consecutive means which come one after the other.

12:03So let's start doing the prime factorization of this number 1729.

12:10Question number 5. We are knowing 1, 7, 2 and 9.

12:16A clue is already there in the question that only the prime numbers will be used to divide it.

12:21It's not an even number. So not divisible by 2.

12:25It's not divisible by 3 either because some of the digits have a look.

12:309 plus 1, 10, 17 and 2, 19. Not divisible by 3, 5.

12:36Let us see if it is divisible by 7.

12:407 into 2. Let me do it here for you. 1729 divided by 7.

12:477 into 2 is 40. Remainder 3. 2 will go down.

12:537 into 4 is 28. Difference 4, this 9 down.

12:58And 7 into 7 is 49. Remainder 0.

13:02That means this number is completely divisible by 7.

13:07I request these questions become easy when we know the tables well.

13:14Tables are going to play a very important role solving here.

13:18Please learn the tables till 20. You can easily solve these questions.

13:22Now this number 247, it's not divisible by 7 once again.

13:28Neither by 11. So next number is 13.

13:32Please have a look. 247 divided by 13.

13:3613 into 1 is 30. Difference 1, 1 and 7.

13:41And 13 into 9 gives you 117.

13:46Now what if you do not know what is the table of 13? You'll get stuck here.

13:50Right? 13 and 19 both have prime number.

13:54So dividing by 13, you get 19 here.

13:58And 19 into 1 is 19. Do not take this one.

14:02So how will you write 1729?

14:051729 is the product of 7, 13 and 19.

14:13Now we have already arranged them in the ascending order.

14:18Question is asking, is there any relationship between any two consecutive factors?

14:23Consecutive means one after the other.

14:26For example, 1, 2, 3. They come one after the other. Consecutive.

14:30Consecutive odd number. 1, 3, 5, 7, so on.

14:35Consecutive even number. 2, 4, 6, 8, so on.

14:40So consecutive means one after the other.

14:437 and 13 are consecutive here in this case.

14:4713 and 19 are consecutive here in this case.

14:52Is there any similarity or any relationship between these factors?

14:57The difference between 13 and 7 is 6. Difference here is 6.

15:02In the similar manner, difference here is 6.

15:05So what you can conclude?

15:07The relationship between two consecutive factors here is this,

15:11that they have a difference of 6.

15:14You can show here, 13 minus 7 is 6 and 19 minus 13 is against.

15:21So that's all about question number 5.

15:24Moving on to question number 6.

15:26The product of three consecutive numbers is always divisible by 6.

15:32You have to verify this statement with the help of some example.

15:36Consecutive, I have just explained you.

15:39Consecutive means one after the other.

15:42But what am I supposed to take the product?

15:45Product means multiplication.

15:47And how many numbers we need to take? 3 numbers.

15:50So it is important to read the question carefully.

15:53Let us see few examples to prove this.

15:57Answer number 6.

15:58Example number 1.

16:00Let me take three consecutive numbers 1, 2, 3.

16:03They are consecutive 3 numbers.

16:06Product means the multiplication.

16:09If I multiply these numbers and divide by 6.

16:133 into 2 is 6.

16:156 into 1 is 6.

16:16Is this 6 divisible by 6?

16:18Yes, it is divisible.

16:20Answer is 1.

16:21Another if I take, let's say 4, 5, 6.

16:26Example number 2.

16:28They are again consecutive 3 consecutive numbers.

16:32I have to take the product and divide by 6.

16:366 up, 6 down.

16:38It is cancelled.

16:39What's your answer?

16:405 into 4.

16:42That's 20.

16:43So we have seen two examples here.

16:46You can take any number you wish to.

16:48Any three consecutive numbers.

16:50And you will find that the product is divisible by 6.

16:54Moving on to question number 7.

16:57The sum of.

16:59Initially in question number 6, we have taken the product.

17:03Product is multiplication.

17:05Question number 7, we are talking about sum.

17:08Sum means addition.

17:10How many numbers do we take then?

17:122.

17:13And the numbers should be consecutive odd numbers.

17:17Please understand each and every term mentioned here.

17:21We have to take how many numbers?

17:242.

17:25They should be consecutive and as well as odd.

17:30And what are we supposed to do with these numbers?

17:33We have to add.

17:34Right?

17:35Again we have to see some example.

17:37Answer number 7.

17:38Example number 1.

17:40First odd number is 1.

17:42Another consecutive is 3.

17:45If I add these numbers, what is the sum?

17:494.

17:50We have to prove that the sum is always divisible by 4.

17:544 is divisible by 4.

17:57Answer is 1.

17:58It is verified here.

17:59Let us take another set of numbers.

18:02If I take first odd number is 3.

18:05Which is the next consecutive odd number?

18:08That is 5.

18:09Question says add the number.

18:11Addition.

18:12The sum is 8.

18:14Now it is also divisible by 4.

18:17Answer is 2.

18:18So we have seen through two examples that a statement holds true.

18:23You can check with another combination of odd numbers.

18:28For example, you can take after 5, we have 5 and 7.

18:33If I add them up, is it giving you 12?

18:36Which is once again divisible by 4.

18:39Answer is 3.

18:40So any two consecutive odd numbers if you add, the sum will always be divisible by 4.

18:47Question number 8 is very easy, oral enough that we have already understood in the beginning of the session only.

18:55In which of the following expression, prime factorization has been done?

19:01Where it is yes.

19:02That means in prime factorization, no composite number should be there.

19:07Have a look.

19:09We have 4 here.

19:10It's a composite number.

19:12Prime factorization.

19:13Nonda.

19:14All the numbers are prime.

19:17And if I see the product also to match.

19:21Triple 8.

19:222 into 2, 4.

19:234 into 2, 8.

19:248 into 7 is 56.

19:26Everything is matching.

19:28This is correct.

19:29C part.

19:302, 5, 7.

19:32All three are prime.

19:345 into 2, 10.

19:3510 into 7, 70.

19:37That is again correct.

19:38Last one we can see 9 is a composite number.

19:42So it is incorrect.

19:44Good to go.

19:45Move to question number 9.

19:48It says 18 is divisible by both 2 and 3.

19:5118 is divisible by 2 and 3 both.

19:55And it is divisible by the product of these numbers.

19:59If I multiply these two, I get 6.

20:02And this 18 is divisible by 6 also.

20:05Question says, if I have the combination of 4 and 6.

20:11If there is a number which is divisible by 4 as well as by 6.

20:17So is it necessary that if I take a product of these numbers.

20:21That is 24.

20:23This number will be divisible by 24 also.

20:26We need to check this.

20:28Every time.

20:29If I am saying yes.

20:30Every time it has to be true.

20:32Let me take an example.

20:35If I take a number 36.

20:38Can it be divided by 4?

20:404 into 9, 36.

20:42Yes.

20:4336 comes in the table of 6.

20:45Divisible by 6.

20:47But if I take the product.

20:49Product is 24.

20:51But 36 is not completely divisible by 24.

20:54So that means it is wrong.

20:56And we have shown the example also.

20:58But why it is true in this case?

21:01It is true in this case because.

21:03When the two numbers are co-prime.

21:07They do not have any common factor between them.

21:10Other than 1.

21:11Only then it is true.

21:13Otherwise not.

21:154 and 6 are not co-prime.

21:17They have 1 and 2.

21:19Both as a common factor.

21:21Okay.

21:22So whenever a combination of co-prime numbers are given.

21:26The product of the number will also divide the given number.

21:30Otherwise not.

21:32Moving on to the last question of this exercise now.

21:36We have to make a smallest number.

21:40Using 4 different prime numbers.

21:43So what we are supposed to do.

21:45Start taking the first 4 prime numbers.

21:48Starting from the smallest one.

21:50We know that the smallest prime number is 2.

21:53Next one is 3.

21:55Next one is 5.

21:57And next one is 7.

21:59Are they 4 prime numbers?

22:01The smallest one.

22:03We have to just take the product of these numbers.

22:06And that is your answer.

22:07Because we have to find the number.

22:10For which we will do prime factorization.

22:12So we have to get 4 different prime factors.

22:15And all should be arranged in the ascending order.

22:18We are making the smallest number.

22:20So take the first 4 smallest prime numbers.

22:23Right.

22:24Another clue.

22:25When there is a combination of 2 and 5.

22:28Make your calculation easier.

22:30Multiply these two first.

22:325 into 2 is 10.

22:343 into 7 is 21.

22:37And what is 21 into 10?

22:39That is 210.

22:40That's your answer.

22:42Right.

22:43So I hope you find this session useful and interesting.

22:47Please don't forget to watch another video.

22:50Where we will be doing exercise 3.6.

22:53And if you have not liked and subscribed.

22:56Please press the like button and subscribe the channel.

22:59Thank you so very much for watching and take care.

23:06See you.