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In theGermanic languages, the number 120 was also formerly known as "one hundred". This "hundred" of sixscore is now obsolete but is described as thelong hundred orgreat hundred in historical contexts.^[1]

In mathematics

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120 is

thefactorial of 5, i.e., $5!=5\cdot 4\cdot 3\cdot 2\cdot 1$ .
the fifteenthtriangular number,^[2] as well as the sum of the first eight triangular numbers, making it also atetrahedral number. 120 is the smallest number to appear six times inPascal's triangle (as all triangular and tetragonal numbers appear in it). Because 15 is also triangular, 120 is adoubly triangular number. 120 is divisible by the first five triangular numbers and the first four tetrahedral numbers. It is the eighthhexagonal number.
The 10thhighly composite,^[3] the 5thsuperior highly composite,^[4]superabundant,^[5] and the 5thcolossally abundant number.^[6] It is also asparsely totient number.^[7] 120 is also the smallest highly composite number with no adjacent prime number, being adjacent to $119=7\cdot 17$ and $121=11^{2}.$ It is also the smallest positive multiple of six not adjacent to a prime.
120 is the firstmultiply perfect number of order three (a 3-perfect ortriperfect number).^[8] The sum of its factors (including one and itself) sum to360, exactly three times 120.Perfect numbers are order two (2-perfect) by the same definition.
120 is the sum of atwin prime pair (59 + 61) and the sum of four consecutiveprime numbers (23 + 29 + 31 + 37), four consecutivepowers 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 anuntouchable number.
The sum ofEuler's totient function $\phi (x)$ over the first nineteen integers is 120.
As 120 is a factorial and one less than a square ( $5!=11^{2}-1$ ), it—with 11—is one of the fewBrown number pairs.
120 appears inPierre 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: ${\textstyle {\frac {777,480}{2879^{2}}}}$ .^{[citation needed]}
The internal angles of a regularhexagon (one where all sides and angles are equal) are all 120 degrees.

In science

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

Threesoap films meet along aPlateau border at 120° angles.

In religion

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The age at whichMoses died (Deut. 34:7).
- By extension, in Jewish tradition, to wish someone a long life, one says, "Live until 120".
Inastrology, 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.^[9]

In other fields

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120 is also:

TT scale, a scale for model trains, is 1:120.
The Standard AC Voltage inUS,Canada,Mexico and some other countries.

References

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^Gordon, E. V. (1957).Introduction to Old Norse. Oxford: Clarendon Press. pp. 292–293. Archived fromthe original on 2016-02-23. Retrieved2022-09-04.
^"A000217 - OEIS".oeis.org. Retrieved2024-11-28.
^"Sloane's A002182 : Highly composite numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"A002201 - OEIS".oeis.org. Retrieved2024-11-28.
^"Sloane's A004394 : Superabundant numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A004490 : Colossally abundant numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A036913 : Sparsely totient numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Sloane's A005820 : 3-perfect numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
^"Astrology And The Black Man".Afro American. January 31, 1970. RetrievedDecember 30, 2010.

Wells, D.The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 135

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