# 120 number

 Template:Numbers (120s) Cardinal 120 one hundred [and] twenty Ordinal 120th one hundred [and] twentieth Factorization ${\displaystyle 2^{3}\cdot 3\cdot 5}$ Divisors 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 Roman numeral CXX Prefixes hecatontakaiicosa- (Greek) Binary 1111000 Octal 170 Duodecimal A0 Hexadecimal 78

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".

## In mathematics

One hundred twenty is the factorial of 5. It is the sum of a twin prime pair (59 + 61) as well as the sum of four consecutive primes (23 + 29 + 31 + 37). It is highly composite and superabundant 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, and it is also a Harshad 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 the first multiply perfect number of order three (a 3-perfect 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.

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:

• Very significant in the Bible, being ten times the number of tribes of Israel. It is the age Moses died at (Deuteronomy 34:7), the cubits of the height of the Temple (2 Chronicles 3:4), the number of princes King Darius set over his kingdom (Daniel 6:2), the number of talents of gold Queen Sheba gave to King Solomon in tribute (1 Kings 10:10), and the weight in shekels of total gold spoons offered by each tribe of Israel (Numbers 7:86).
• A medium film format introduced by Kodak in 1901 and still in use in 2004.
• 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.
• The designation of some spur routes of Interstate 20 in the US.
• The year AD 120 or 120 BC.
• An old alternative meaning of the word Hundred.