Number reference
37 explained.
37: thirty-seven, prime; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- thirty-seven
- Classification
- prime
- Factors
- 1, 37
- Prime factorization
- 37
- Square root
- 6.082763
- Cube root
- 3.332222
- Binary
- 100101
- Octal
- 45
- Hexadecimal
- 25
- Roman numeral
- XXXVII
- Digit sum
- 10
- Digital root
- 1
What makes 37 notable
- Prime. 37 is prime: it has exactly two divisors, 1 and itself, so it cannot be split into equal whole-number groups any other way.
37 in everyday use
Normal human body temperature is about 37 degrees Celsius, the figure on every thermometer's red line. Thirty-seven is the atomic number of rubidium, used in atomic clocks. In the mathematics of optimal stopping, the "37 percent rule" says to look at roughly the first 37 percent of options before committing, because 1/e is about 0.368. Thirty-seven also turns up unusually often when people are asked to name a "random" number between 1 and 100.
Thirty-seven is the twelfth prime and an isolated one: neither 35 nor 39 is prime. Multiply it by 3 and you get 111, so 37 divides every three-digit repdigit — 222, 333, up to 999. It is the sum of two squares, 1 + 36, and a centered hexagonal number, 1 + 6 + 12 + 18. In the decimal expansion of 1/37 the digits repeat every three places: 0.027027….
Nearby numbers
How to read this page
Because 37 is prime, the factor list stops at 1 and 37 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 37 in its prime factorisation inherits it from here.
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