496
496 is the third perfect number: it equals the sum of its proper divisors.
- Even
- Composite
Where 496 fits
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.
496 is part of
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
- Triangular number
- Perfect number
- Happy number
- Hexagonal number
Related numbers & connections
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 →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