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)
Issues in Q1,Q4
1)3ways
2)8ways
3)2ways
4)12ways
5)
6)5ways
7)can’t be written
8)3ways
9)2ways
10)cant be written
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
done…
done.
done
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
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
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
1.1
2.8
3.2
4.12
5.8
6.5
7.no ways
8.3
9.2
10.
no ways
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
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
1.3ways
2.8ways
3.2ways
4.12ways
5.8ways
6.4ways
7.Cannot be written
8.3ways
9.2ways
10.Cannot be written
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
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
done!!
done sir but not 9 no.
done
done
done
done…!!