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Amicable Pair Finder

See if a number forms an amicable pair with the sum of its proper divisors.

How to use

  1. Enter your values in the fields above.
  2. Press Calculate to see your result instantly.
  3. Use the Share button to copy a link to your result.

About this calculator

Two numbers form an amicable pair when the sum of each number’s proper divisors (all divisors excluding the number itself) equals the other number. The smallest and most famous example, known since antiquity, is 220 and 284: the proper divisors of 220 (1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110) add up to 284, and the proper divisors of 284 (1, 2, 4, 71, 142) add up to 220.

Amicable numbers are a close cousin of perfect numbers (where a number’s proper divisors sum to itself, like 6 and 28) and have been studied since Pythagorean times, later expanded by mathematicians like Fermat, Descartes and Euler, who found several more pairs by algebraic formula rather than brute search. Today they are mostly a recreational and educational number-theory topic, useful for exploring divisor-sum functions.

This calculator computes the sum of proper divisors for any number you enter, checks whether that sum’s own proper divisors lead back to your original number, and confirms whether the pair is truly amicable.

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