Number analysis
9,999
9,999 is a composite odd number that factors as 3^2 × 11 × 101.
9,999 is a composite odd number that factors as 3^2 × 11 × 101.
The number itself
- Value
- 9,999
- Digits
- 4
- Digit sum
- 36
- Reversed
- 9,999
- Palindrome
- Yes
9 + 9 + 9 + 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
- Prime factorisation
- 3^2 × 11 × 101
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 9,973 ← → 10,007
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2 × 11 × 101.
3 distinct prime factors, 4 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 34 between them.
Divisors
- Sum of divisors σ(n)
- 15,912
- Aliquot sum
- 5,913
- Classification
- Deficient
- Euler totient φ(n)
- 6,000
1, 3, 9, 11, 33, 99, 101, 303, 909, 1,111, 3,333, 9,999
The proper divisors — everything except n itself.
Its proper divisors fall short by 4,086.
How many integers from 1 to n share no factor with n.
Sums and additive structure
- Sum of two squares
- No
- Sum of three squares
- No
- Sum of four squares
- Yes
A prime congruent to 3 mod 4 divides it an odd number of times, which rules it out.
Excluded by Legendre: it has the form 4^a(8b + 7).
Lagrange's four-square theorem: every non-negative integer is, without exception.
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
- No
- Kaprekar number
- Yes
- Collatz trajectory
- 91 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 36.
Peaks at 101,248 along the way.
Written other ways
- Binary
- 10011100001111
- Octal
- 23417
- Hexadecimal
- 270F
- Base 36
- 7PR
- In words
- nine thousand nine hundred and ninety-nine
- Scientific notation
- 9.999 × 10^3
Standard Roman numerals only run from 1 to 3,999.
Is 9,999 a prime number?
Composite — it factors as 3^2 × 11 × 101.
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.