Amicable Numbers Checker

About this calculator

Two numbers are amicable if each equals the sum of the other's proper divisors (its aliquot sum — all divisors excluding the number itself). The classic pair is 220 and 284: the proper divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) sum to 284, and the proper divisors of 284 (1, 2, 4, 71, 142) sum to 220. This calculator finds a number's aliquot sum, identifies its potential amicable partner, and checks whether the two truly form a pair.

Amicable numbers were studied as far back as the Pythagoreans, who saw them as a symbol of friendship, and later extended by mathematicians like Fermat, Descartes and Euler, who found dozens more pairs through algebraic rules such as Thābit ibn Qurra's formula. Today they're mostly a recreational and educational topic — number theory enthusiasts, math teachers and students use calculators like this to explore divisor sums, perfect numbers (a number equal to its own aliquot sum) and sociable number chains.