Perfect Number Checker
Number (≤ 100,000)
Known perfect numbers: 6, 28, 496, 8128, 33550336…
A perfect number equals the sum of its proper divisors (excluding itself). The first perfect numbers are 6, 28, 496, 8128. All known perfect numbers are even; it is unknown whether odd perfect numbers exist.
- 1Sum all divisors except n itself
- 26: 1+2+3 = 6 ✓
- 328: 1+2+4+7+14 = 28 ✓
- 4Abundant: divisor sum > n; Deficient: divisor sum < n
n = 28=Divisors 1,2,4,7,14 — Sum = 28 (Perfect!)
n = 12=Divisors 1,2,3,4,6 — Sum = 16 > 12 (Abundant)
| n | Divisor Sum | Type |
|---|---|---|
| 6 | 6 | Perfect |
| 12 | 16 | Abundant |
| 8 | 7 | Deficient |
| 28 | 28 | Perfect |
| 496 | 496 | Perfect |
References
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