|Cardinal||one hundred twenty|
(one hundred and twentieth)
|Factorization||23× 3 × 5|
|Divisors||1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120|
120 (one hundred [and] twenty) 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".
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.
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.
120 is divisible by the number of primes below it, 30 in this case. However there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number.
The sum of Euler's totient function φ(x) over the first nineteen integers is 120.
120 figures in Pierre de 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. Leonhard Euler also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, 777480 / 28792.
- The cubits of the height of the Temple building (II Chronicles 3:4)
- The age at which Moses died (Deut. 34:7).
- By extension, in Jewish tradition, to wish someone a long life, one says, "Live until 120"
- The number of Men of the Great Assembly who canonized the Books of the Tanakh and formulated the Jewish prayers
- The number of talents of gold that the Queen of Sheba gave to Solomon in tribute (I Kings 10:10)
- The number of princes King Darius set over his kingdom (Daniel 6:2)
- The summed weight in shekels of the gold spoons offered by each tribal prince of Israel (Num. 7:86).
- In astrology, when two planets in a person's chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring good luck in the person's life.
In other fields
120 is also:
- The medical telephone number in China
- In Austria, the telephone number "to report a car breakdown on the highway.
- In the US Army, a common diameter for a mortar in mm (M120).
- TT scale, a scale for model trains, is 1:120.
- 120 film is a medium format film developed by Kodak.
- 120 (film), a 2008 Turkish film
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 135