Number analysis
496
The third perfect number, and a dimension that appears in heterotic string theory.
The third perfect number, and a dimension that appears in heterotic string theory.
The number itself
- Value
- 496
- Digits
- 3
- Digit sum
- 19
- Reversed
- 694
- Palindrome
- No
4 + 9 + 6
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 694.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2^4 × 31
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 491 ← → 499
Divisible by 2.
Composite — it factors as 2^4 × 31.
2 distinct prime factors, 5 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 8 between them.
Divisors
- Aliquot sum
- 496
- Classification
- Perfect
1, 2, 4, 8, 16, 31, 62, 124, 248, 496
The proper divisors — everything except n itself.
Its proper divisors sum to exactly itself.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- No
- Sum of four squares
- Yes
- Goldbach pair
- 5 + 491
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
Lagrange's four-square theorem: every non-negative integer is, without exception.
The smallest pair of primes summing to n. Goldbach’s conjecture says one always exists; it remains unproven.
Shapes and sequences
- Triangular number
- Yes — the 31st
- Hexagonal number
- Yes — the 16th
Digit curiosities
- Happy number
- Yes
- Harshad number
- No
- Collatz trajectory
- 110 steps to 1
Repeatedly summing the squares of its digits reaches 1.
Not divisible by its digit sum 19.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 111110000
- Octal
- 760
- Hexadecimal
- 1F0
- Base 36
- DS
- Roman numerals
- CDXCVI
- In words
- four hundred and ninety-six
- Scientific notation
- 4.96 × 10^2
Is 496 a prime number?
Composite — it factors as 2^4 × 31.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 496 their own way.
- Morse code
- · · · · − − − − − · − · · · ·
- Devanagari
- ४९६
- Tamil
- ௪௱௯௰௬
- Thai
- ๔๙๖
References
Further reading: Wikipedia · Wikidata
Notations, naming and the links above come from Wikidata, whose structured data is dedicated to the public domain under CC0-1.0. Retrieved 2026-10-07.