Number reference
36 explained.
36: thirty-six, composite, perfect square; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- thirty-six
- Classification
- composite
- Factors
- 1, 2, 3, 4, 6, 9, 12, 18, 36
- Prime factorization
- 2 × 2 × 3 × 3
- Square root
- 6
- Cube root
- 3.301927
- Binary
- 100100
- Octal
- 44
- Hexadecimal
- 24
- Roman numeral
- XXXVI
- Digit sum
- 9
- Digital root
- 9
What makes 36 notable
- Perfect square. 36 = 6², so a square of side 6 has an area of 36.
- Triangular number. 36 is the 8th triangular number: it is the sum 1 + 2 + … + 8, the count of items in a triangle with 8 rows.
- Highly composite. 36 has 9 divisors — more than any smaller positive number. That is why numbers like this get chosen for units of time, angle, and packaging.
36 in everyday use
Thirty-six inches make a yard, and 36 is the atomic number of krypton. A European roulette wheel has the numbers 1 to 36 plus a zero, and a roll of 35 mm film traditionally held 36 exposures. The exterior angle of a regular ten-sided polygon is 36 degrees, and the points of a five-pointed star are 36 degrees each. In Jewish tradition the 36 righteous people, the lamed-vavniks, sustain the world.
Thirty-six is six squared and also the eighth triangular number, 1 + 2 + … + 8, making it the smallest number after 1 that is both square and triangular. It has nine divisors — 1, 2, 3, 4, 6, 9, 12, 18, 36 — and is highly composite, with more divisors than any smaller number. Its digits, 3 and 6, are the second and third triangular numbers, and 36 itself is the sum of the first three cubes, 1 + 8 + 27.
Nearby numbers
How to read this page
The factor list shows every way 36 splits into equal whole-number groups — 9 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 36 for contexts that do not use decimal.
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