Number reference
48 explained.
48: forty-eight, composite, highly composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- forty-eight
- Classification
- composite
- Factors
- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Prime factorization
- 2 × 2 × 2 × 2 × 3
- Square root
- 6.928203
- Cube root
- 3.634241
- Binary
- 110000
- Octal
- 60
- Hexadecimal
- 30
- Roman numeral
- XLVIII
- Digit sum
- 12
- Digital root
- 3
What makes 48 notable
- Highly composite. 48 has 10 divisors — more than any smaller positive number. That is why numbers like this get chosen for units of time, angle, and packaging.
48 in everyday use
Forty-eight hours is two days, the classic deadline. It is the atomic number of cadmium, once common in rechargeable batteries. The contiguous United States number 48 states, Bach's Well-Tempered Clavier contains 48 preludes and fugues across its two books, and a pinochle deck has 48 cards. Four dozen is 48, and a day has 48 half-hours.
Forty-eight is 2⁴ × 3 and has ten divisors — 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 — more than any smaller number, which makes it highly composite. It is the smallest number with exactly ten divisors. It is also 6 × 8 and 4 × 12, and in geometry it is the number of symmetries of a cube once reflections are counted alongside the 24 rotations.
Nearby numbers
How to read this page
The factor list shows every way 48 splits into equal whole-number groups — 10 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 48 for contexts that do not use decimal.
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