Number analysis
113
113 is a prime number — divisible only by 1 and itself.
113 is a prime number — divisible only by 1 and itself.
The number itself
- Value
- 113
- Digits
- 3
- Digit sum
- 5
- Reversed
- 311
- Palindrome
- No
1 + 1 + 3
Digit sum repeated until one digit remains; equals n mod 9 (with 9 for multiples of 9).
Reverses to 311.
Parity and primality
- Parity
- Odd
- Prime
- Yes
- Squarefree
- Yes
- Möbius μ(n)
- -1
- Sophie Germain prime
- Yes — 2n+1 = 227 is also prime
- Nearest primes
- 109 ← → 127
Leaves remainder 1 on division by 2.
Divisible only by 1 and itself.
1 distinct prime factor, 1 with multiplicity.
No prime divides it twice.
(−1) to the power of 1 distinct prime factors.
A gap of 18 between them.
Divisors
- Aliquot sum
- 1
- Classification
- Deficient
1, 113
The proper divisors — everything except n itself.
Its proper divisors fall short by 112.
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
7² + 8² = 113
Legendre's three-square theorem allows it.
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
- Collatz trajectory
- 12 steps to 1
Summing the squares of its digits falls into the 4 → 16 → 37 → … → 4 cycle.
Not divisible by its digit sum 5.
Peaks at 340 along the way.
Written other ways
- Binary
- 1110001
- Octal
- 161
- Hexadecimal
- 71
- Base 36
- 35
- Roman numerals
- CXIII
- In words
- one hundred and thirteen
- Scientific notation
- 1.13 × 10^2
Is 113 a prime number?
Yes. 113 has no divisors other than 1 and itself.
Nearby numbers
Other numeral systems
Beyond the bases and Roman numerals above, these notations write 113 their own way.
- Morse code
- · − − − − · − − − − · · · − −
- Devanagari
- ११३
- Tamil
- ௱௰௩
- Thai
- ๑๑๓
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.