Perfect Number Check Calculator

Reviewed by the CalculatorHub team, edited by James Graham. Last verified 25 June 2026.

A perfect number is a positive whole number that equals the sum of its own proper divisors, the divisors smaller than the number itself. The first perfect number is six, whose proper divisors one, two and three add up to six; the next is twenty-eight, then four hundred ninety-six. This calculator takes a whole number and tells you whether it is perfect by computing the sum of its divisors and checking whether that sum equals twice the number, which is the same as saying the proper divisors total the number. The calculator also shows the proper divisors and their sum so you can see the test directly. Perfect numbers have fascinated mathematicians since antiquity and are tied to Mersenne primes through a classical theorem of Euclid and Euler. They are rare: only a handful are known among small numbers, and all known perfect numbers are even. Students, number-theory enthusiasts and puzzle solvers use this check to explore the idea. Enter a whole number to get the verdict immediately; the input is a plain integer, so no decimal formatting applies. Every figure here is computed deterministically from the rule shown below, with a worked example that reconciles exactly to the calculator so you can follow each step yourself.