Product of Two factors
To find the number as the products of two factors, use the following steps :
Step1: Write Prime factorisation of given number i.e. convert the number in the form ap bq cr
where a, b,c are prime numbers and the p,q,r are natural numbers as their respective powers.
Step 2:Find Number of factors which can be expressed as( p+1)(q+1)(r+1).
Step 3: Number of ways to express the number as a product of two numbers is exactly half its number of factors i.e.½ *(p+1)(q+1)(r+1).
Let’s have an example on this :
Example 1: In how many ways can you express 54 as a product of two of its factors?
Solution:  We will do the above problem step by step:
Step 1: Prime factorization of 54 i.e. we write 54 = 2133
Step 2: Number of factors of 54 will be (1+1)(3+1) = 2 x 4= 8
Step 3:  Hence number of ways to express 54 as a product of two numbers is exactly half its number of factors i.e. ½ *8 = 4 ways.
In fact we can list these 4 ways as well
Factors of 54 are 1,2,3,6,9, 18,27,54.
Now it is very simple to find the factors from 1 to 9 but it is difficult to find the ones that are greater than 10. So number of ways to express 54 as a product of two of its factors is
1 x 54 = 54
2 x 27 = 54
3 x 18 = 54
6 x 9   = 54
Example 2: In how many ways you can express 120  as a product of two of its factors?
Solution:
Step 1: Prime factorization of 120 i.e. we write 120  = 233151
Step 2: Number of factors of 120 will be (3+1)(1+1)(1+1) = 4 x 2 x2 = 16
Step 3:  Hence number of ways to express 120 as a product of two numbers is exactly half its number of factors i.e. ½ *16 = 8
In fact we can list these 8 ways as well
Factors of 120 are 1,2,3,4,5,6,8,10,12,15,18,24,30,40,60,120.
So number of ways to express 120 as a product of two of its factors is
1 x 120 = 120
2 x 60 = 120
3 x 40 = 120
4 x 30 = 120
5 x 24 = 120
6 x 20 = 120
8 x 15 = 120
10 x 12=120