Number reference
83 explained.
83: eighty-three, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- eighty-three
- Classification
- prime
- Factors
- 1, 83
- Prime factorization
- 83
- Square root
- 9.110434
- Cube root
- 4.362071
- Binary
- 1010011
- Octal
- 123
- Hexadecimal
- 53
- Roman numeral
- LXXXIII
- Digit sum
- 11
- Digital root
- 2
What makes 83 notable
- Prime. 83 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
83 in everyday use
Eighty-three is the atomic number of bismuth, long considered the heaviest stable element until 2003, when its single isotope was shown to decay with a half-life of about twenty billion billion years — over a billion times the age of the universe. Bismuth crystals grow into iridescent staircases, and the compound bismuth subsalicylate is the pink active ingredient in Pepto-Bismol.
Eighty-three is the 23rd prime and both a Sophie Germain prime, since 2 × 83 + 1 = 167 is prime, and a safe prime, since (83 − 1) / 2 = 41 is prime. It is the sum of three consecutive primes, 23 + 29 + 31, and of five consecutive primes, 11 + 13 + 17 + 19 + 23. In binary it is 1010011.
Nearby numbers
How to read this page
Because 83 is prime, the factor list stops at 1 and 83 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 83 in its prime factorisation inherits it from here.
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