# 120 (number)

Short description: Natural number
 ← 119 120 121 →
Cardinalone hundred twenty
Ordinal120th
(one hundred twentieth)
Numeral systemCentovigesimal
Factorization23 × 3 × 5
Divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Greek numeralΡΚ´
Roman numeralCXX
Binary11110002
Ternary111103
Quaternary13204
Quinary4405
Senary3206
Octal1708
DuodecimalA012
Vigesimal6020
Base 363C36
The 120-cell (or hecatonicosachoron) is a convex regular 4-polytope consisting of 120 dodecahedral cells.

120 (one hundred [and] twenty) is the natural number following 119 and preceding 121.

In the Germanic languages, the number 120 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.[1]

## In mathematics

120 is

• the factorial of 5, i.e., $\displaystyle{ 5!=5\cdot 4\cdot 3\cdot 2\cdot 1 }$.
• the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is the smallest number to appear six times in Pascal's triangle (as all triangular and tetragonal numbers appear in it). Because 15 is also triangular, 120 is a doubly triangular number. 120 is divisible by the first five triangular numbers and the first four tetrahedral numbers. It is the eighth hexagonal number.
• highly composite,[2] superior highly composite, superabundant,[3] and colossally abundant.[4] 120 is the smallest number with exactly 16 divisors. It is also a sparsely totient number.[5] 120 is also the smallest highly composite number as well as the first multiple of six with no adjacent prime number, being adjacent to $\displaystyle{ 119=7\cdot 17 }$ and $\displaystyle{ 121=11^2. }$
• 120 is the first multiply perfect number of order three (a 3-perfect or triperfect number).[6] 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 the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of two (8 + 16 + 32 + 64), and four consecutive powers of three (3 + 9 + 27 + 81).
• 120 is divisible by the number of primes below it (30). However, there is no integer that has 120 as the sum of its proper divisors, making 120 an untouchable number.
• The sum of Euler's totient function $\displaystyle{ \phi (x) }$ over the first nineteen integers is 120.
• As 120 is a factorial and one less than a square ($\displaystyle{ 5!=11^{2}-1 }$), it—with 11—is one of the few Brown number pairs.
• 120 appears 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, when multiplied by 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. He failed to find an integer, but he did find a fraction that meets the other conditions: $\displaystyle{ \frac {777,480}{2879^{2}} }$.[citation needed]
• The internal angles of a regular hexagon (one where all sides and angles are equal) are all 120 degrees.
• There are 120 primes between 3,000 and 4,000.

## In science

120 is the atomic number of unbinilium, an element yet to be discovered.

In electrical engineering, each line of the three-phase system are 120 degrees apart from each other.

Three soap films meet along a Plateau border at 120° angles.

## In religion

• 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 to the person's life.[7]

## In sports

• The height (in inches) of a regulation hoop in the National Basketball Association.[8] (In metric units, this is about 3.05 m)

## 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.[9]
• 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, a 2008 Turkish film
• The Israeli national legislature, the Knesset, has 120 seats.
• China Airlines Flight 120

• List of highways numbered 120
• United Nations Security Council Resolution 120

## References

1. Gordon, E. V. (1957). Introduction to Old Norse. Oxford: Clarendon Press. pp. 292–293. Retrieved 2022-09-04.
2. "Sloane's A002182 : Highly composite numbers". OEIS Foundation.
3. "Sloane's A004394 : Superabundant numbers". OEIS Foundation.
4. "Sloane's A004490 : Colossally abundant numbers". OEIS Foundation.
5. "Sloane's A036913 : Sparsely totient numbers". OEIS Foundation.
6. "Sloane's A005820 : 3-perfect numbers". OEIS Foundation.
7. The Game Court, National Basketball Association, retrieved 2014-04-07.
8. Porter, Darwin; Danforth Prince (2009). Frommer's Austria. Hoboken, New Jersey: Frommer's. p. 482. ISBN 978-0-470-39897-5.
• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 135