Number reference
113 explained.
113: one hundred thirteen, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred thirteen
- Classification
- prime
- Factors
- 1, 113
- Prime factorization
- 113
- Square root
- 10.630146
- Cube root
- 4.834588
- Binary
- 1110001
- Octal
- 161
- Hexadecimal
- 71
- Roman numeral
- CXIII
- Digit sum
- 5
- Digital root
- 5
What makes 113 notable
- Prime. 113 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
113 in everyday use
One hundred thirteen is the denominator of one of the best simple approximations to pi. The fraction 355/113 equals 3.14159292, agreeing with pi to six decimal places, and no fraction with a smaller denominator does better. The Chinese mathematician Zu Chongzhi recorded it in the fifth century, and it is still taught as a memory aid: write the odd digits 1, 1, 3, 3, 5, 5 and split them in the middle. In practical engineering it is close enough for almost any calculation done without a calculator.
The number is prime and unusually robust about it. Rearrange its digits and every arrangement is prime: 113, 131, and 311 all pass, which makes 113 a permutable prime. Double it and add one and you get 227, also prime, so 113 is a Sophie Germain prime as well. It closes a twin-prime-free gap: after 113 the next prime is 127, a jump of 14 that no gap between consecutive primes below 500 exceeds.
Nearby numbers
How to read this page
Because 113 is prime, the factor list stops at 1 and 113 itself, so it cannot be shared into equal whole-number groups. That is also what makes it useful as a building block: every larger number with 113 in its prime factorisation inherits it from here.
Percentage calculator · Fraction calculator · Browse Number Explorer