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
- Scientific notation
- 4.960 × 10^2
Roman numerals
C D X C V I
CDXCVI uses the subtractive pair XC: ten before a hundred — a hundred minus ten.
Binary
1 1 1 1 1 0 0 0 0
1 × 256 + 1 × 128 + 1 × 64 + 1 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 496
Octal
7 6 0
7 × 64 + 6 × 8 + 0 × 1 = 496
Hexadecimal
1 f 0
1 × 256 + f × 16 + 0 × 1 = 496
Read as powers of two: 256 + 128 + 64 + 32 + 16 = 496.
In historical numeral systems
Egyptian
4 coils of rope, 9 hobbles, 6 strokes
4 × 100 + 9 × 10 + 6 × 1 = 496. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
8 vertical wedges (sixties place), 1 corner wedge + 6 vertical wedges (units place)
8 × 60 + 16 = 496. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
upsilon, then koppa, then stigma, marked as a numeral
upsilon-koppa-stigma + keraia
upsilon + koppa + stigma written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
tav, then tsadi, then vav
tav-tsadi-vav
tav (400) + tsadi (90) + vav (6) = 496, written in descending order.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
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 →Science
In 1984 Michael Green and John Schwarz showed that superstring theory is free of certain quantum inconsistencies only if its gauge symmetry group has dimension 496 — a condition satisfied by exactly two groups, SO(32) and E₈ × E₈. The result set off the period known as the first superstring revolution. That the required dimension is also the third perfect number is a coincidence with no known significance, and is routinely quoted as though it were meaningful.
DocumentedSciencePeriod: 1984
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.
DocumentedMathematics496 = 2⁴ × 31, and like every even perfect number after 6 it has a digital root of 1: repeatedly summing its digits gives 4 + 9 + 6 = 19, then 1 + 9 = 10, then 1. The pattern follows from the Euclid form 2^(p−1) × (2^p − 1) with p an odd prime, and holds for 28, 496, 8128 and every one found since. It is a genuine consequence rather than an observed coincidence.
DocumentedMathematics
Common questions
What is a perfect number?
One that equals the sum of its own proper divisors. 496's are 1, 2, 4, 8, 16, 31, 62, 124 and 248, and they total 496. Euclid proved that 2^(p−1) × (2^p − 1) is perfect whenever 2^p − 1 is prime, and Euler showed every even perfect number has that form — so they correspond exactly to Mersenne primes, which is why only around fifty are known. Whether any odd perfect number exists is unresolved after two thousand years.
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. XC is subtractive: ten before a hundred — a hundred minus ten. Written additively it would be CCCCLXXXXVI, which Roman inscriptions used freely — the strict subtractive form is a later convention.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 3 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026