# Sum of Divisors

In number theory, many formulas exist that we never think of. The first topic I wrote about number theory is to find the number of divisors an integer has. This time let’s talk about finding the sum of those divisors without listing them individually.

Formula:

Given a positive integer with prime factor the sum of its divisors ( ** S_{n}**) can be calculated using the formula,

*Worked Problems 1:*

Find the sum of divisors of 12.

Solution:

It is easy to check that the answer is correct by listing down all the divisors of 12 which is {1,2,3,4,6,12}.

*Worked Problem 2:*

Find the sum of divisors of 5400.

Solution:

*Worked Problem 3:*

The sum of divisors of an integer ** N** is 7623.

**can be written in the form of**

*N***where x and y are all positive integers. What is**

*2*^{x}3^{y}**?**

*N*Solution:

We take note of the following facts;

is odd and is even.

Also

Since is even, 2 is one of its factors. And take note that x and y are positive integers. By inspection;

Consequently,

Since