A perfect number equals the sum of its proper divisors (excluding itself). 6 = 1+2+3. 28 = 1+2+4+7+14. Only ~51 are known, all even (it's unknown if odd perfect numbers exist). They follow the formula 2^(p−1) × (2^p − 1) when 2^p − 1 is a Mersenne prime.
How to Use
Enter any positive integer to check:
- Classification: Perfect, abundant, or deficient
- Divisors: All proper divisors listed
- Sum: Compared against the number
Known Perfect Numbers
- 6 (p=2)
- 28 (p=3)
- 496 (p=5)
- 8,128 (p=7)
- 33,550,336 (p=13)
Number Types
- Perfect: σ(n)−n = n (ratio = 1.0)
- Abundant: σ(n)−n > n (ratio > 1.0)
- Deficient: σ(n)−n < n (ratio < 1.0)
Step-by-Step Instructions
- 1Enter a positive integer.
- 2Check if it's perfect.
- 3View all proper divisors.
- 4See the divisor sum.
- 5Try known perfect numbers.