Sum of Factors Calculator

Sum of factors calculator calculates the total sum of all divisors of a given number.

How to Calculate the Sum of Factors

To calculate the sum of factors, we first need to find all the factors of a number and then sum them up.

For example, the factors of 50 are: 1, 2, 5, 10, 25, and 50.
The sum of these factors is:
          1+2+5+10+25+50=93.

This method works well for small numbers.
However, for larger numbers, such as 1200, calculating all the factors manually would take a lot of time. Instead, we use prime factorization to break down the number.

For example:
          1200 = 2⁴ x 3 x 5²

Using the formula for the sum of divisors based on prime factorization:
           (2⁰ + 2¹ + 2² + 2³ + 2⁴) x (3⁰ + 3¹)x (5⁰ + 5¹ + 5²)

This simplifies to:
           (1 + 2 + 4 + 8 + 16)×(1 + 3)×(1 + 5 + 25)
           =31 x 4 x 31
           =3844.