Sum of proper divisors of a perfect number

Statement

A number is perfect if it equals the sum of its proper divisors (those less than the number). Compute the sum of the proper divisors of $496$ and verify that $496$ is perfect.

Solution

$496=2^4\cdot 31$. Its proper divisors are $1,2,4,8,16,31,62,124,248$. Their sum: $1+2+4+8+16+31+62+124+248=\boxed{496}.$ Since the sum equals the number, $496$ is perfect.