Number analysis
81
81 is a composite odd number that factors as 3^4.
81 is a composite odd number that factors as 3^4.
The number itself
- Value
- 81
- Digits
- 2
- Digit sum
- 9
- Reversed
- 18
- Palindrome
- No
8 + 1
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 18.
Parity and primality
- Parity
- Odd
- Prime
- No
- Squarefree
- No
- Prime power
- 3^4
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 79 ← → 83
Leaves remainder 1 on division by 2.
Composite — it factors as 3^4.
1 distinct prime factor, 4 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 4 between them.
Divisors
- Aliquot sum
- 40
- Classification
- Deficient
1, 3, 9, 27, 81
The proper divisors — everything except n itself.
Its proper divisors fall short by 41.
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
0² + 9² = 81
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Square number
- Yes — the 9th
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 22 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 81 ÷ 9 = 9.
Peaks at 244 along the way.
Written other ways
- Binary
- 1010001
- Octal
- 121
- Hexadecimal
- 51
- Base 36
- 29
- Roman numerals
- LXXXI
- In words
- eighty-one
- Scientific notation
- 8.1 × 10^1
Is 81 a prime number?
Composite — it factors as 3^4.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 81 their own way.
- Greek (alphabetic)
- ΠΑʹ
- Babylonian cuneiform
- 𒐕𒎙𒐕
- Tamil
- ௮௰௧
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.