Number analysis
1,089
Reverse-and-subtract any three-digit number with distinct ends, add the reverse, and you always get 1089.
Reverse-and-subtract any three-digit number with distinct ends, add the reverse, and you always get 1089.
The number itself
- Value
- 1,089
- Digits
- 4
- Digit sum
- 18
- Reversed
- 9,801
- Palindrome
- No
1 + 0 + 8 + 9
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 9,801.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3^2 × 11^2
- Squarefree
- No
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 1,087 ← → 1,091
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2 × 11^2.
2 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Every prime factor appears at least squared.
Zero, because a squared prime divides n.
A gap of 4 between them.
Divisors
- Sum of divisors σ(n)
- 1,729
- Aliquot sum
- 640
- Classification
- Deficient
1, 3, 9, 11, 33, 99, 121, 363, 1,089
The proper divisors — everything except n itself.
Its proper divisors fall short by 449.
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 + 33² = 1,089
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 33rd
Digit curiosities
- Happy number
- No
- Harshad number
- No
- Collatz trajectory
- 44 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 18.
Peaks at 3,268 along the way.
Written other ways
- Binary
- 10001000001
- Octal
- 2101
- Hexadecimal
- 441
- Base 36
- U9
- Roman numerals
- MLXXXIX
- In words
- one thousand and eighty-nine
- Scientific notation
- 1.089 × 10^3
Is 1,089 a prime number?
Composite — it factors as 3^2 × 11^2.
Nearby numbers
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.