Perfect Number Calculator

A number is classified here by comparing it to the sum of its own proper divisors — every divisor smaller than the number itself, always including 1. When that sum equals the number, the calculator labels it Perfect; the default value of 28 is one of the four smallest examples, since 1 plus 2 plus 4 plus 7 plus 14 adds back up to exactly 28. When the sum exceeds the number, it is Abundant, and Abundance reports how far over it runs; when the sum falls short, it is Deficient, and Abundance reports the shortfall as a negative figure — so Abundance is one signed number that tells you both which category applies and by how much it applies.

The divisor search only tests candidates up to the square root of the number, pairing each divisor it finds with its complement (the number divided by that divisor), which is why the search stays fast even near the ten-million ceiling this tool allows. What the tool does not attempt is any deeper classification: it will not tell you whether a perfect number is even or odd — every one discovered so far is even, but no one has proved an odd one is impossible — and it sorts every non-perfect number into simply abundant or deficient without flagging how rare true perfect numbers actually are among the integers this calculator can reach; there are only a handful below ten million.