Perfect Number Calculator
Classify a number as perfect, abundant or deficient.
What is Perfect Numbers?
A number is perfect when its proper divisors — every divisor except itself — add up to it: 28 = 1 + 2 + 4 + 7 + 14. Below that sum it is deficient, above it abundant. Only 51 perfect numbers are known, every one of them even, and whether an odd one exists is an open question; the even ones all have Euclid's form 2^(p−1) × (2^p − 1), where 2^p − 1 is a Mersenne prime.
How it works
The divisors are found by trial division to √n, the largest is dropped to leave the proper divisors, and their sum is compared with the number itself. The comparison is written out (1 + 2 + 4 + 7 + 14 = 28) because the sum is the definition, not a step toward it, and the nearest perfect numbers above and below are named so the answer has somewhere to sit.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
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