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496

496 is the third perfect number: it equals the sum of its proper divisors.

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Where 496 fits

Where 496 fits: Mathematics, Related numbersMathematics: Triangular number, Perfect number, Happy number, Hexagonal number. Related numbers: 8128, 28.MathematicsTriangular numberPerfect numberHappy numberHexagonal numberRelated numbers812828496
496 connects to 2 worlds: mathematics, related numbers.

Why 496 is special

496 belongs to a set so small that all of its known members can be listed. Its proper divisors — 1, 2, 4, 8, 16, 31, 62, 124, 248 — sum to exactly 496. It follows 6 and 28, and Euclid's construction explains why: 496 = 2⁴ × (2⁵ − 1), and 31 is prime. Whether any odd perfect number exists is still unresolved after more than two thousand years.

Factors & digit properties

Divisors (10)
1, 2, 4, 8, 16, 31, 62, 124, 248, 496
Prime factorisation
2^4 × 31
Digit sum
19
Digital root
1

Representations

Decimal
496
Binary
111110000
Octal
760
Hexadecimal
1f0
Roman numeral
CDXCVI
Scientific notation
4.960 × 10^2

Other mathematical patterns

Related numbers & connections

Documented appearance
The third and fourth perfect numbers, and the last two the ancient world knew. Both follow Euclid's construction from a Mersenne prime, and the gap after 8128 lasted well over a thousand years before the fifth was recorded.

The third and fourth perfect numbers, and the last two the ancient world knew. Both follow Euclid's construction from a Mersenne prime, and the gap after 8128 lasted well over a thousand years before the fifth was recorded.

View 8128

Numbers Around Us

  • appears alongside8128
    why?

    Strength 0.50, confidence "high".

  • appears alongside28
    why?

    Strength 0.50, confidence "high".

How is 496 connected to another number? →

Mathematics

  • Euclid proved that if 2ᵖ − 1 is prime then 2ᵖ⁻¹ × (2ᵖ − 1) is perfect, and Euler later showed every even perfect number has that form. So perfect numbers are in exact correspondence with Mersenne primes, which is why only around fifty are known: finding a new one means finding a new Mersenne prime.

    DocumentedMathematics

Common questions

Is 496 a prime number?

No, 496 is not prime.

What are the factors of 496?

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.

What is 496 in Roman numerals?

496 in Roman numerals is CDXCVI.

About this page's data

Mathematical facts:computed directly from the number's value — nothing to source or verify externally.

Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.

Last reviewed: 3 August 2026

496 — Meaning, Facts and Properties | Numberwise