Proper Divisors Calculator

About this calculator

A proper divisor of a number is any divisor other than the number itself — for 12, that's 1, 2, 3, 4, and 6. Adding proper divisors together gives the aliquot sum, a value ancient Greek mathematicians used to classify numbers: if the aliquot sum equals the number, it's a perfect number (like 6 = 1+2+3); if the sum is higher, it's abundant; if lower, it's deficient.

This calculator finds proper divisors by testing factor pairs up to the square root of the number, then reports the count and aliquot sum. Number theorists, math teachers, and puzzle enthusiasts use these ideas to study perfect and amicable numbers, and the same divisor-counting logic underlies parts of cryptography and computer science.