Find the sum of the factors of 3600.

Question: Find the sum of the factors of 3600.

Solution:
If k = a^x × b^y
then, a, and b must be prime number.
Sum of all factors = (a⁰ + a¹ + a² + ….. + a^x) (b⁰ + b¹ + b² + ….. + b^y)

Now,
3600 = 2⁴ × 3² × 5²
Sum of factors = (2⁰ + 2¹ + 2² + 2³ + 2⁴) (3⁰ + 3¹ + 3²) (5⁰ + 5¹ + 5²)
= (1 + 2 + 4 + 8 + 16) (1 + 3 + 9) (1 + 5 + 25)
= 31 × 13 × 31
= 12493

∴ required sum is 12493