120 (number)
120 (one hundred twenty in American English; one hundred and twenty in British English) is the natural number following 119 and preceding 121. 120 was known as "the great hundred", especially prior to the year 1700, from the Teutonic Hundert which equalled 120. The number 100, now known commonly as "one hundred" was then known as "the small hundred".
| |||
| Cardinal | One hundred [and] twenty | ||
| Ordinal | 120th | ||
| Factorization | |||
| Divisors | 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 60 | ||
| Roman numeral | CXX | ||
| Binary | 1111000 | ||
| Hexadecimal | 78 | ||
| Table of contents |
|
2 In other fields 3 Other numbers in the 120s |
In mathematics
One hundred twenty is a highly composite number, and the factorial of 5. It is also the sum of a twin prime pair (59 + 61) as well as the sum of four consecutive primes (23 + 29 + 31 + 37). 120 is the smallest number to appear six times in Pascal's triangle, and it is also a Harshad number.
It is a triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. Also, it's a hexagonal number.
120 is divisible by the number of primes below it, 30 in this case.
One hundred twenty figures in Fermat's modified Diophantine problem as the largest known integer of the sequence 1, 3, 8, 120. Fermat wanted to find another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Euler also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480 / 287922.
The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degrees.
In other fields
One hundred twenty is also:
Other numbers in the 120s
One hundred twenty-one has its own article.
122 now has its own article.
One hundred twenty-three (123, CXXIII) is the natural number following one hundred twenty-two and preceding one hundred twenty-four. It is a Lucas number and a composite number, and its factorization is
One hundred twenty-three is also:
One hundred twenty-four (124, CXXIV) is the natural number following one hundred twenty-three and preceding one hundred twenty-five. It is a composite number, and its factorization is
It is the sum of eight consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29). It is a nontotient since there is no integer with 124 coprimes below it.
One hundred twenty-four is also:
One hundred twenty-five (125, CXXV) is the natural number following one hundred twenty-four and preceding one hundred twenty-six. It is a composite number, and its factorization is
One hundred twenty-five is also:
One hundred twenty-six has its own article.
One hundred twenty-seven has its own article.
One hundred twenty-eight has its own article.
One hundred twenty-nine (129, CXXIX) is the natural number following one hundred twenty-eight and preceding one hundred thirty. It is a composite number, and its factorization is
This number is the sum of the first ten prime numbers.
One hundred twenty-nine is also:
- The designation of a spur route of Interstate 29 in Sioux City, Iowa.
- The year AD 129 or 129 BC.