Number reference
107 explained.
107: one hundred seven, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred seven
- Classification
- prime
- Factors
- 1, 107
- Prime factorization
- 107
- Square root
- 10.34408
- Cube root
- 4.747459
- Binary
- 1101011
- Octal
- 153
- Hexadecimal
- 6B
- Roman numeral
- CVII
- Digit sum
- 8
- Digital root
- 8
What makes 107 notable
- Prime. 107 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
107 in everyday use
One hundred seven is the atomic number of bohrium, a synthetic element first confirmed in Darmstadt, Germany, in 1981 and named after the physicist Niels Bohr. It appears in physics in another guise too: 2 raised to the power 107, minus one, is a Mersenne prime, a fact established by Ralph Ernest Powers in 1914 when checking such numbers by hand was a major undertaking. That makes 107 one of the special exponents behind the enormous primes that record-setting computer searches still hunt for today.
One hundred seven is itself prime and the first member of a twin-prime pair with 109. It is also a safe prime: subtract one and halve it and you get 53, which is prime as well. Safe primes matter in cryptography because groups of that size resist certain shortcuts in the discrete logarithm problem. Its digits sum to 8, and it is the 28th prime, sitting in the sparse stretch between 103 and 109.
Nearby numbers
How to read this page
Because 107 is prime, the factor list stops at 1 and 107 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 107 in its prime factorisation inherits it from here.
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