Sum of Factors of a Number using Prime Factorization

Given a number N. The task is to find the sum of all factors of the given number N.

Examples:  

Input : N = 12
Output : 28
All factors of 12 are: 1,2,3,4,6,12

Input : 60
Output : 168 

Approach: 

Suppose N = 1100, the idea is to first find the prime factorization of the given number N. 
Therefore, the prime factorization of 1100 = 2² * 5² * 11.
So, the formula to calculate the sum of all factors can be given as, 

A dry run is as shown below as follows: 

(2⁰ + 2¹ + 2²) * (5⁰ + 5¹ + 5²) * (11⁰ + 11¹) 
(upto the power of factor in factorization i.e. power of 2 and 5 is 2 and 11 is 1.) 
= (1 + 2 + 2²) * (1 + 5 + 5²) * (1 + 11) 
= 7 * 31 * 12 
= 2604
So, the sum of all factors of 1100 = 2604 

Below is the implementation of the above approach: 

Sum of the factors is : 28

Time Complexity: O(N)

Auxiliary Space: O(n) // an extra n sized array has been created.