Number analysis
9
9 is a composite odd number that factors as 3^2.
9 is a composite odd number that factors as 3^2.
The number itself
- Value
- 9
- Digits
- 1
- Digit sum
- 9
- Reversed
- 9
- Palindrome
- Yes
9
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reads the same in both directions.
Parity and primality
- Parity
- Odd
- Prime
- No
- Squarefree
- No
- Semiprime
- Yes
- Prime power
- 3^2
- Powerful
- Yes
- Möbius μ(n)
- 0
- Nearest primes
- 7 ← → 11
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2.
1 distinct prime factor, 2 with multiplicity.
At least one prime appears squared.
A product of exactly two primes, counted with multiplicity.
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
- 4
- Classification
- Deficient
1, 3, 9
The proper divisors — everything except n itself.
Its proper divisors fall short by 5.
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
- Sum of two cubes
- 1³ + 2³
0² + 3² = 9
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 3rd
Digit curiosities
- Happy number
- No
- Armstrong number
- Yes, trivially
- Harshad number
- Yes
- Kaprekar number
- Yes
- Collatz trajectory
- 19 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Every single-digit number equals itself raised to the first power, so all ten qualify trivially.
Divisible by its digit sum 9 — 9 ÷ 9 = 1.
Peaks at 52 along the way.
Written other ways
- Binary
- 1001
- Octal
- 11
- Base 36
- 9
- In words
- nine
- Scientific notation
- 9 × 10^0
Is 9 a prime number?
Composite — it factors as 3^2.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 9 their own way.
- Greek (alphabetic)
- Θʹ
- Tamil
- ௯
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.