Perfect Number Checker

How it works

1. 1Enter any whole number ≥ 1 into the input field.
2. 2The checker finds all proper divisors — every positive factor smaller than the number itself — and sums them.
3. 3If the divisor sum equals the original number (e.g. 1 + 2 + 3 = 6), the number is perfect; otherwise it is not.

Use cases

• Verify classic perfect numbers such as 6, 28, 496, and 8128 in number-theory coursework.
• Explore the factorisation structure of any integer to deepen understanding of divisibility.
• Quickly confirm or disprove perfect-number candidates in recreational mathematics.

Frequently asked questions

What is a perfect number?

A perfect number is a positive integer that equals the sum of all its proper divisors — every positive divisor except itself. The smallest examples are 6 (1 + 2 + 3) and 28 (1 + 2 + 4 + 7 + 14).

How many perfect numbers are known?

Only 51 perfect numbers have been discovered, and all are even. Each takes the form 2^(p−1) × (2^p − 1) where 2^p − 1 is a Mersenne prime. Whether any odd perfect number exists remains an open problem.

Why is 1 not a perfect number?

1 has no proper divisors (its only divisor is itself, which is excluded), so its proper-divisor sum is 0, not 1. The definition requires the sum to equal the number, so 1 fails.