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Cardinal | one hundred twenty | |||
Ordinal | 120th (one hundred twentieth) |
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Factorization | 23× 3 × 5 | |||
Divisors | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 | |||
Roman numeral | CXX | |||
Binary | 11110002 | |||
Ternary | 111103 | |||
Quaternary | 13204 | |||
Quinary | 4405 | |||
Senary | 3206 | |||
Octal | 1708 | |||
Duodecimal | A012 | |||
Hexadecimal | 7816 | |||
Vigesimal | 6020 | |||
Base 36 | 3C36 |
120, read as one hundred twenty, is the natural number following 119 and preceding 121.
In English and other Germanic languages, it was also formerly known as "one hundred". This "hundred" of six score is now obsolete, but is described as the long hundred or great hundred in historical contexts.
120 is the factorial of 5, and the sum of a twin prime pair (59 + 61). 120 is the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of 2 (8 + 16 + 32 + 64), and four consecutive powers of 3 (3 + 9 + 27 + 81). It is highly composite,superabundant, and colossally abundant number, with its 16 divisors being more than any number lower than it has, and it is also the smallest number to have exactly that many divisors. It is also a sparsely totient number. 120 is the smallest number to appear six times in Pascal's triangle. 120 is also the smallest multiple of 6 with no adjacent prime number, being adjacent to 119 = 7 × 17 and 121 = 112.
It is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers.
120 is the first multiply perfect number of order three (a 3-perfect or triperfect number). The sum of its factors (including one and itself) sum to 360; exactly three times 120. Note that perfect numbers are order two (2-perfect) by the same definition.