Number reference
150 explained.
150: one hundred fifty, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred fifty
- Classification
- composite
- Factors
- 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
- Prime factorization
- 2 × 3 × 5 × 5
- Square root
- 12.247449
- Cube root
- 5.313293
- Binary
- 10010110
- Octal
- 226
- Hexadecimal
- 96
- Roman numeral
- CL
- Digit sum
- 6
- Digital root
- 6
What makes 150 notable
- Factor structure. 150 breaks down into 3 distinct primes (2, 3, 5) and has 12 divisors in total, so it can be split into equal whole-number groups 10 ways beyond 1 and itself.
150 in everyday use
One hundred fifty is Dunbar's number, the anthropologist Robin Dunbar's estimate of how many stable social relationships a person can maintain. He derived it from primate brain sizes and found it echoed in hunter-gatherer villages, army companies, and the size at which firms often reorganise. A sesquicentennial is a 150th anniversary, and the Book of Psalms contains 150 psalms in most Bibles. In Roman numerals it is CL, and 150 grams is a common serving size in nutrition tables.
Arithmetically, 150 is 2 × 3 × 5², so its divisors are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150 — twelve in all. It is the interior angle, in degrees, of a regular twelve-sided polygon, since 180 − 360 ÷ 12 = 150, and a 150-degree turn leaves you 30 degrees short of facing backwards. It is not a triangular or square number, but 150 is the sum of eight consecutive primes, from 7 to 37.
Nearby numbers
How to read this page
The factor list shows every way 150 splits into equal whole-number groups — 12 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 150 for contexts that do not use decimal.
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