Number analysis
63
63 is a composite odd number that factors as 3^2 × 7.
63 is a composite odd number that factors as 3^2 × 7.
The number itself
- Value
- 63
- Digits
- 2
- Digit sum
- 9
- Reversed
- 36
- Palindrome
- No
6 + 3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 36.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3^2 × 7
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 61 ← → 67
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2 × 7.
2 distinct prime factors, 3 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 6 between them.
Divisors
- Aliquot sum
- 41
- Classification
- Deficient
1, 3, 7, 9, 21, 63
The proper divisors — everything except n itself.
Its proper divisors fall short by 22.
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
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.
Shapes and sequences
- Figurate shapes
- None
Not triangular, square, pentagonal, hexagonal, cubic, Fibonacci, Lucas, Catalan, factorial or a power of two.
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 107 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 63 ÷ 9 = 7.
Peaks at 9,232 along the way.
Written other ways
- Binary
- 111111
- Octal
- 77
- Hexadecimal
- 3F
- Base 36
- 1R
- Roman numerals
- LXIII
- In words
- sixty-three
- Scientific notation
- 6.3 × 10^1
Is 63 a prime number?
Composite — it factors as 3^2 × 7.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 63 their own way.
- Greek (alphabetic)
- ΞΓʹ
- Babylonian cuneiform
- 𒐕𒐗
- Tamil
- ௬௰௩
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.