Number reference
57 explained.
57: fifty-seven, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- fifty-seven
- Classification
- composite
- Factors
- 1, 3, 19, 57
- Prime factorization
- 3 × 19
- Square root
- 7.549834
- Cube root
- 3.848501
- Binary
- 111001
- Octal
- 71
- Hexadecimal
- 39
- Roman numeral
- LVII
- Digit sum
- 12
- Digital root
- 3
What makes 57 notable
- Semiprime. 57 = 3 × 19, a product of exactly two primes. That gives it just four divisors, so it splits into equal groups in only two non-trivial ways.
57 in everyday use
Heinz has advertised "57 varieties" since 1896, a figure Henry Heinz picked because he liked the sound of it rather than because it counted anything. Fifty-seven is the atomic number of lanthanum, the first of the rare-earth lanthanides. In mathematics it is jokingly called the Grothendieck prime, after a story in which the great algebraist offered 57 as an example of a prime. It is not one.
Fifty-seven is 3 × 19. It is a repunit in base 7, since 49 + 7 + 1 = 57 is written 111 there. It is also a Leyland number, 2⁵ + 5², one of the numbers of the form xʸ + yˣ. It has four divisors — 1, 3, 19, and 57 — and in binary it is 111001. Sitting between the even numbers 56 and 58 with no obvious small factor beyond 3, it is easy to mistake for a prime, which is exactly what makes the Grothendieck story funny.
Nearby numbers
How to read this page
The factor list shows every way 57 splits into equal whole-number groups — 4 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 57 for contexts that do not use decimal.
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