120 (number)
From Wikipedia, the free encyclopedia
| Cardinal | 120 one hundred [and] twenty |
| Ordinal | 120th one hundred [and] twentieth |
| Factorization |  |
| Divisors | 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 |
| 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". It is also known as 'twelvety' according to the number naming system invented by J. R. R. Tolkien (c.f. eleventy).
[edit] In mathematics
120 is the factorial of 5. It is the sum of a twin prime pair (59 + 61) as well as the sum of four consecutive prime numbers (23 + 29 + 31 + 37) and of 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 the first multiply perfect number of order three (a 3-perfect number, triperfect). 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 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 / 28792.
The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120 degrees.
120 is a Harshad number in base 10.
[edit] In religion
- The age at which Moses died (Deut. 34:7). "Ad me'ah v'esrim shanah" (עד מאה ועשרים שנה) is a common Hebrew blessing for longevity
- The number of Men of the Great Assembly who canonized the Books of the Tanakh and formulated the Jewish prayers
- The weight in shekels of the gold spoons offered by each tribe of Israel (Num. 7:86).
- The cubits of the height of the Temple building (II Chronicles 3:4)
- The number of talents of gold Queen Sheba gave to King Solomon in tribute (I Kings 10:10)
- The number of princes King Darius set over his kingdom (Daniel 6:2)
[edit] In other fields
120 is also:
- An old alternative meaning of the word Hundred, and the meaning of the Teutonic word Hundert
- A medium film format introduced by Kodak in 1901 and still in use today.
- 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 time's most controversial book ever, 120 Days of Sodom
- The year AD 120 or 120 BC
