120 (number)

← 119 121 → 120
← 120 121 122 123 124 125 126 127 128 129 → List of numbers — Integers ← 100 110 120 130 140 150 160 170 180 190 →
Cardinal	one hundred [and] twenty
Ordinal	120th (one hundred [and] twentieth)
Numeral system	120
Factorization	$2^3 \cdot 3 \cdot 5$
Divisors	1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Roman numeral	CXX
Binary	11110002
Octal	1708
Duodecimal	A012
Hexadecimal	7816

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. 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).

In mathematics

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 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 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 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.

In science

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

In astronomy observers note when planets are 120 degrees apart.^{[citation needed]}

In religion

• The cubits of the height of the Temple building (II Chronicles 3:4)
• 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 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)
• The weight in shekels of the gold spoons offered by each tribe 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.^[1]

In sports

• The height in inches of a regulation basketball hoop^{[citation needed]}
• In Super Mario 64 for the Nintendo 64 120 is the maximum number of power stars a player can get, and the max number of shine sprites in Super Mario Sunshine^{[citation needed]}
• In the NCAA, the number of Division 1-A Schools.

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.^[2]
• In the US Army, a common diameter for a mortar in mm (M120).

See also

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

References

1. ^ "Astrology And The Black Man". Afro American. January 31, 1970. http://news.google.com/newspapers?id=FCEmAAAAIBAJ&sjid=Bv4FAAAAIBAJ&pg=4399,615262&dq=astrology+planets+120+degrees+trine&hl=en. Retrieved December 30, 2010. 
2. ^ 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