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Home/Mathematics/Number Theory/Perfect Number Checker
Math CalculatorNumber Theory

Perfect Number Checker

Determine whether a given positive integer is a perfect number. A perfect number equals the sum of its proper divisors (all divisors excluding itself).

Updated 2025-01-154 min readCalzyra Math Team
HomeMathnumber theoryPerfect Number Checker

Perfect Number Checker

Determine whether a given positive integer is a perfect number. A perfect number equals the sum of its proper divisors (all divisors excluding itself).

Formulan is perfect if σ(n) = 2n (or equivalently, sum of proper divisors = n)

Enter Values

Enter an integer to check if it is a perfect number

About This Formula

A perfect number equals the sum of its proper divisors. The first few are 6, 28, 496, 8128. All known even perfect numbers have the form 2^(p−1)(2^p − 1) where 2^p − 1 is a Mersenne prime.

Formula & Methodology

How this calculator works

n is perfect if σ(n) = 2n (or equivalently, sum of proper divisors = n)

A perfect number equals the sum of its proper divisors. The first few are 6, 28, 496, 8128. All known even perfect numbers have the form 2^(p−1)(2^p − 1) where 2^p − 1 is a Mersenne prime.

Frequently Asked Questions

Common questions about this calculator

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