How to find the number of factors of a Number

The method to find the Numbers of factors of a number can be illustrated with an example:

Q 1. Find the number of different divisors of the number 1150?

Solution:
1150 can be written as a multiplication of prime numbers as

1150 = 2 x 5 x 5 x 23
or
1150 =   2 × 5² x 23
we have to add 1 to the power of each of prime factors and then multiply them to get the required answer.
Power of 2 is 1. Add 1 to 1 to get (1+1) =2
Power of 5 is 2. Add 1 to 2 to get (2+1) = 3
Power of 23 is 1. Add 1 to 1 to get (1+1)  = 2

Now, the number of different divisors of 1150 are  2 x 3 x 2=12

Q2. Find the number of divisors of the number 144500 excluding itself and unity.

Solution:
144500 = 2²×5³×17²
Now,
add 1 to the power of 2 to get (2+1)  = 3
add 1 to the power of 3 to get (3+1)  = 4
add 1 to the power of 2 to get (2+1)  = 3

Therefore number of divisors of 144500 are (3)(4)(3) = 36
And excluding unity and itself the number of divisors comes out to be 36-2 = 34