Number analysis
90
90 is a composite even number that factors as 2 × 3^2 × 5.
90 is a composite even number that factors as 2 × 3^2 × 5.
The number itself
- Value
- 90
- Digits
- 2
- Digit sum
- 9
- Reversed
- 9
- Palindrome
- No
9 + 0
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 9.
Parity and primality
- Parity
- Even
- Prime
- No
- Prime factorisation
- 2 × 3^2 × 5
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 89 ← → 97
Divisible by 2.
Composite — it factors as 2 × 3^2 × 5.
3 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 8 between them.
Divisors
- Aliquot sum
- 144
- Classification
- Abundant
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The proper divisors — everything except n itself.
Its proper divisors overshoot by 54.
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
- Goldbach pair
- 7 + 83
3² + 9² = 90
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
- 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
- 17 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 90 ÷ 9 = 10.
Peaks at 136 along the way.
Written other ways
- Binary
- 1011010
- Octal
- 132
- Hexadecimal
- 5A
- Base 36
- 2I
- In words
- ninety
- Scientific notation
- 9.0 × 10^1
Is 90 a prime number?
Composite — it factors as 2 × 3^2 × 5.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 90 their own way.
- Greek (alphabetic)
- Ϟʹ
- Babylonian cuneiform
- 𒐕𒌍
- Tamil
- ௯௰
References
Further reading: Wikipedia · MathWorld · 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.