Number reference
33 explained.
33: thirty-three, composite, repdigit; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- thirty-three
- Classification
- composite
- Factors
- 1, 3, 11, 33
- Prime factorization
- 3 × 11
- Square root
- 5.744563
- Cube root
- 3.207534
- Binary
- 100001
- Octal
- 41
- Hexadecimal
- 21
- Roman numeral
- XXXIII
- Digit sum
- 6
- Digital root
- 6
What makes 33 notable
- Repdigit. 33 is written with a single repeated digit, so it is divisible by the repunit of the same length.
33 in everyday use
Long-playing vinyl records spin at 33⅓ revolutions per minute, a speed chosen by Columbia in 1948 to fit a symphony on one side. Thirty-three is the atomic number of arsenic. The human spine has 33 vertebrae, counting the fused ones in the sacrum and coccyx. Christian tradition puts Jesus's age at his death at 33. In 2010 the world watched as 33 Chilean miners were rescued after 69 days underground.
Thirty-three is a repdigit, 3 × 11, and the sum of the first four factorials: 1 + 2 + 6 + 24. It is the largest number that cannot be written as a sum of distinct triangular numbers; everything above it can be. It is also the first of three consecutive numbers — 33, 34, 35 — that each have exactly four divisors, the smallest such run. In binary it is 100001, a palindrome.
Nearby numbers
How to read this page
The factor list shows every way 33 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 33 for contexts that do not use decimal.
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