# Expressing a Number as a product of two natural numbers

And applications

This video deals with the basics of finding the number of ways of writing a number as a product of two natural numbers. It explains the difference between the number being a perfect square and not being a perfect square.

What you should already know to understand this well ” How to find the number of factors of a given number ”

### The Basics

Once you are through with the video, you could try the following three questions:

1. Find the number of ways of writing 315 as a difference of two perfect squares?

2. Find the number of ways of writing 120 as a difference of two perfect squares?

You should pay special attention to the difference between the above two questions.

3. Find the number of natural number solutions to

### Basics Applied for Q1 .

The videos in the parts 2, 3 and 4 of the topic will give the detailed solutions to the above questions.

### Practice Questions:

1. In how many number of ways can 68 be expressed as a product of two natural numbers? (Ans 3 ways)

2. In how many number of ways can 2025 be written as a product of two natural numbers? (Ans 8 ways)

3. In how many number of ways can 625 be written as a product of two distinct natural numbers? (Ans 2 ways)

4. x,y are two natural numbers, such that x*y = 360. How many possible pairs of x,y exist? (Ans 12 ways)

5. In how many ways can 945 be written as a difference of two perfect squares? (Ans 8 ways)

6. Find the number of ways in which 441 can be written as a difference of two perfect squares. (Ans 4 ways)

7. In how many number of ways can 322 be written as a difference of two perfect squares? (Ans Can’t be written)

8. In how many number of ways can 252 be written as a difference of two perfect squares? ( Ans 3 ways)

9. In how many ways can 516 be written as a difference of two perfect squares? (Ans 2 ways)

10. In how many ways can 58 be written as a difference of two perfect squares? (Ans Can’t be written)

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### 71 Responses to CAT quant with Chandra-4

1. saloni_anand says:

Issues in Q1,Q4

2. Damini says:

1)3ways
2)8ways
3)2ways
4)12ways
5)
6)5ways
7)can’t be written
8)3ways
9)2ways
10)cant be written

3. Damini says:

1)3ways
2)8ways
3)2ways
4)12ways
5)8ways
6)5ways
7)can’t be written
8)3ways
9)2ways
10)cant be written

4. alokdokewar says:

done…

5. shreya.patwari says:

done.

6. miniswitz says:

done

7. Pals says:

1. 3 ways
2. 8 ways
3. 2 ways
4. 12 ways
5. 8 ways
6. 4 ways
7. Cannot be written
8. 3 ways
9. 2 ways
10. Cannot be written

8. Pranati says:

1. 3 ways
2. 8 ways
3. 2 ways
4. 12 ways
5. 8 ways
6. 4 ways
7. cannot be written
8. 3 ways
9. 2 ways
10. cannot be written

9. Neha a oswal says:

1. 3 ways
2.8 ways
3.2 ways
4.12ways
5. 8 ways
6.4 ways
7. cannot be written
8. 3 ways
9.2 ways
10.cannot be written

10. surbhim says:

1.1
2.8
3.2
4.12
5.8
6.5
7.no ways
8.3
9.2
10.
no ways

11. hitesh6293 says:

1. 3 ways
2. 8 ways
3. 2 ways
4. 12 ways
5. 8 ways
6. 4 ways
7. Cannot be written
8. 3 ways
9. 2 ways
10. Cannot be written

12. akshaybhalgat says:

1.3 ways
2.8 ways
3. 2 ways
4.12 ways
5.8 ways
6.4 ways
7. Cannot be written
8. 3 ways
9.2 ways
10. Cannot be written

13. vinal_gandhi says:

1.3ways
2.8ways
3.2ways
4.12ways
5.8ways
6.4ways
7.Cannot be written
8.3ways
9.2ways
10.Cannot be written

14. Siddhi Satpute says:

1.3 ways
2.8 ways
3.2 ways
4.12 ways
5.8 ways
6.4 ways
7.can’t be written
8.3 ways
9.2 ways
10. can’t be written

15. Shifa says:

1:3 ways
2:8 ways
3:2 ways
4:12 ways
5:8 ways
6:4 ways
7:can’t be written
8:3 ways
9:2 ways
10:can’t be written

16. tanu.agrawal says:

done!!

17. abhinaykumar says:

done sir but not 9 no.

18. abhijeet says:

done

19. ankita.agrawal says:

done

20. pulkitmittal says:

done

21. saket93 says:

done…!!