Number analysis
117
117 is a composite odd number that factors as 3^2 × 13.
117 is a composite odd number that factors as 3^2 × 13.
The number itself
- Value
- 117
- Digits
- 3
- Digit sum
- 9
- Reversed
- 711
- Palindrome
- No
1 + 1 + 7
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 711.
Parity and primality
- Parity
- Odd
- Prime
- No
- Prime factorisation
- 3^2 × 13
- Squarefree
- No
- Möbius μ(n)
- 0
- Nearest primes
- 113 ← → 127
Leaves remainder 1 on division by 2.
Composite — it factors as 3^2 × 13.
2 distinct prime factors, 3 with multiplicity.
At least one prime appears squared.
Zero, because a squared prime divides n.
A gap of 14 between them.
Divisors
- Aliquot sum
- 65
- Classification
- Deficient
1, 3, 9, 13, 39, 117
The proper divisors — everything except n itself.
Its proper divisors fall short by 52.
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
6² + 9² = 117
Legendre's three-square theorem allows it.
Lagrange's four-square theorem: every non-negative integer is, without exception.
Shapes and sequences
- Pentagonal number
- Yes — the 9th
Digit curiosities
- Happy number
- No
- Harshad number
- Yes
- Collatz trajectory
- 20 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Divisible by its digit sum 9 — 117 ÷ 9 = 13.
Peaks at 352 along the way.
Written other ways
- Binary
- 1110101
- Octal
- 165
- Hexadecimal
- 75
- Base 36
- 39
- Roman numerals
- CXVII
- In words
- one hundred and seventeen
- Scientific notation
- 1.17 × 10^2
Is 117 a prime number?
Composite — it factors as 3^2 × 13.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 117 their own way.
- Morse code
- · − − − − · − − − − − − · · ·
- Devanagari
- ११७
- Tamil
- ௱௰௭
- Thai
- ๑๑๗
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.