Number analysis
89
89 is a prime number — divisible only by 1 and itself.
89 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 89
- Digits
- 2
- Digit sum
- 17
- Reversed
- 98
- Palindrome
- No
8 + 9
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 98.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Sophie Germain prime
- Yes — 2n+1 = 179 is also prime
- Nearest primes
- 83 ← → 97
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 14 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 89
The proper divisors — everything except n itself.
Its proper divisors fall short by 88.
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
5² + 8² = 89
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Fibonacci number
- Yes — index 11
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 30 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 17.
Peaks at 304 along the way.
Written other ways
- Binary
- 1011001
- Octal
- 131
- Hexadecimal
- 59
- Base 36
- 2H
- Roman numerals
- LXXXIX
- In words
- eighty-nine
- Scientific notation
- 8.9 × 10^1
Is 89 a prime number?
Yes. 89 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 89 their own way.
- Greek (alphabetic)
- ΠΘʹ
- Babylonian cuneiform
- 𒐕𒎙𒐝
- Tamil
- ௮௰௯
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.