How is 496 a perfect number?

Answer 1

The factors of 496 (excluding itself) are:

1, 2, 4, 8, 16, 31, 62, 124, 248 whose sum is 496.

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The prime factorization of 496 is

496 = 24*31. If we take σ(496) (sum of all divisors of 496), this is equal to

σ(496) = σ(24)σ(31) (this is a useful property, σ(ab) = σ(a)σ(b) for relatively prime a,b)

Since σ(24) = 1+2+4+8+16 = 31 and σ(31) = 1+31 = 32,

σ(496) = 31*32 = 2(496), so 496 is perfect.