Number analysis
64
Squares on a chessboard, and 2⁶ — the wheat-and-chessboard problem doubles across all of them.
Squares on a chessboard, and 2⁶ — the wheat-and-chessboard problem doubles across all of them.
The number itself
- Value
- 64
- Digits
- 2
- Digit sum
- 10
- Reversed
- 46
- Palindrome
- No
6 + 4
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 46.
Parity and primality
- Parity
- Even
- Prime
- No
- Squarefree
- No
- Prime power
- 2^6
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 61 ← → 67
Divisible by 2.
Composite — it factors as 2^6.
1 distinct prime factor, 6 with multiplicity.
At least one prime appears squared.
A single prime raised to a power.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 6 between them.
Divisors
- Aliquot sum
- 63
- Classification
- Deficient
1, 2, 4, 8, 16, 32, 64
The proper divisors — everything except n itself.
Its proper divisors fall short by 1.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- Yes
- Sum of three squares
- Yes
- Sum of four squares
- Yes
- Sum of two cubes
- 0³ + 4³
- Goldbach pair
- 3 + 61
0² + 8² = 64
Legendre's three-square theorem allows it.
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
- Square number
- Yes — the 8th
- Perfect cube
- Yes — 4³
- Power of two
- Yes — 2^6
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 6 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 10.
Peaks at 64 along the way.
Written other ways
- Binary
- 1000000
- Octal
- 100
- Hexadecimal
- 40
- Base 36
- 1S
- Roman numerals
- LXIV
- In words
- sixty-four
- Scientific notation
- 6.4 × 10^1
Is 64 a prime number?
Composite — it factors as 2^6.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 64 their own way.
- Greek (alphabetic)
- ΞΔʹ
- Babylonian cuneiform
- 𒐕𒐘
- Tamil
- ௬௰௪
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.