Number reference
108 explained.
108: one hundred eight, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- one hundred eight
- Classification
- composite
- Factors
- 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Prime factorization
- 2 × 2 × 3 × 3 × 3
- Square root
- 10.392305
- Cube root
- 4.762203
- Binary
- 1101100
- Octal
- 154
- Hexadecimal
- 6C
- Roman numeral
- CVIII
- Digit sum
- 9
- Digital root
- 9
What makes 108 notable
- Factor structure. 108 breaks down into 2 distinct primes (2, 3) and has 12 divisors in total, so it can be split into equal whole-number groups 10 ways beyond 1 and itself.
108 in everyday use
One hundred eight recurs in the religions of South and East Asia. Hindu and Buddhist prayer beads, the mala, traditionally have 108 beads, and mantras are commonly repeated 108 times; Japanese Buddhist temples ring their bells 108 times at New Year. The reasons offered vary by tradition, and the number is treated as significant rather than derived from any single doctrine. In sport it has a precise role: a regulation baseball is stitched with exactly 108 double stitches of waxed red thread, a figure fixed in the rules.
Arithmetically, 108 is 2² × 3³, and it can be written as 1¹ × 2² × 3³, the first three numbers each raised to its own power. It is the interior angle, in degrees, of a regular pentagon, which makes it the angle at every corner of the pentagons on a soccer ball and in the pentagram. It is also nine dozen and the number of degrees in three-tenths of a full turn.
Nearby numbers
How to read this page
The factor list shows every way 108 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 108 for contexts that do not use decimal.
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