learn.howToCalculate
learn.whatIsHeading
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.
Formel
n is perfect if σ(n) = 2n, where σ(n) is sum of all divisors
- n
- the number being tested
- σ(n)
- sum of all divisors of n (including n) (integer)
Trin-for-trin guide
- 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
Løste eksempler
Input
n = 28
Resultat
Divisors 1,2,4,7,14 — Sum = 28 (Perfect!)
Input
n = 12
Resultat
Divisors 1,2,3,4,6 — Sum = 16 > 12 (Abundant)
Ofte stillede spørgsmål
What is the smallest perfect number?
6: its divisors are 1, 2, 3, 6, and 1+2+3 = 6 (sum of proper divisors equals n).
Is 28 a perfect number?
Yes: divisors are 1, 2, 4, 7, 14, 28, and 1+2+4+7+14 = 28.
How many perfect numbers are known?
51 perfect numbers are known (as of 2024). All known ones are even and quite rare.
Klar til at beregne? Prøv den gratis Perfect Number Checker-beregner
Prøv det selv →