120, read as one hundred ndtwenty, is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal ...

following

119 119 may refer to: * 119 (number), a natural number * 119 (emergency telephone number) * AD 119, a year in the 2nd century AD * 119 BC, a year in the 2nd century BC * 119 (album), 2012 * 119 (NCT song) *119 (Show Me the Money song) * 119 (film), a ...

and preceding 121. In the

Germanic languages The Germanic languages are a branch of the Indo-European language family spoken natively by a population of about 515 million people mainly in Europe, North America, Oceania and Southern Africa. The most widely spoken Germanic language, E ...

, 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 The long hundred, also known as the great hundred or twelfty, is the number 120 (in base-10 Arabic numerals) that was referred to as "hundred" in Germanic languages prior to the 15th century, and is now known as one hundred twenty, or six score. ...

or great hundred in historical contexts.

In mathematics

120 is * the factorial of 5 i.e. 5 × 4 × 3 × 2 × 1 * the fifteenth

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

, as well as the sum of the first eight triangular numbers, making it also a

tetrahedral number A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is, ...

. 120 is the smallest number to appear six times in

Pascal's triangle In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although o ...

(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 5 triangular numbers and the first 4 tetrahedral numbers. It is the eighth

hexagonal number A hexagonal number is a figurate number. The ''n''th hexagonal number ''h'n'' is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so ...

. * highly composite, superior 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 In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, ''n'', is sparsely totient if for all ''m'' > ''n'', :\varphi(m)>\varphi(n) where \varphi is Euler's totient function. The first few sparsely toti ...

. 120 is also the smallest highly composite number as well as the first multiple of 6 with no adjacent prime number, being adjacent to 119 = 7 × 17 and 121 = 11². * 120 is the first

multiply perfect number Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...

of order three (''a 3-perfect'' or '' triperfect number''). The sum of its factors (including one and itself) sum to 360; exactly three times 120. Note that

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. ...

s are order two (''2-perfect'') by the same definition. * 120 is the sum of a

twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...

pair (59 + 61) and the sum of four consecutive

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

s (23 + 29 + 31 + 37), four consecutive powers of 2 (8 + 16 + 32 + 64), and four consecutive powers of 3 (3 + 9 + 27 + 81). *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 An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...

. * The sum of Euler's totient function φ(''x'') over the first nineteen integers is 120. * As it is a factorial and one less than a square, it, with 11, is one of the few

Brown number Brocard's problem is a problem in mathematics that asks to find integer values of n and m for which n!+1 = m^2, where n! is the factorial. It was posed by Henri Brocard in a pair of articles in 1876 and 1885, and independently in 1913 by Sriniv ...

pairs. *120 appears in

Pierre de Fermat Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he ...

'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 Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

also searched for this number, but failed to find it, but did find a fractional number that meets the other conditions, . *The internal angles of a regular

hexagon In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has ...

(one where all sides and all angles are equal) are all 120

degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...

In science

120 is the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...

unbinilium Unbinilium, also known as eka-radium or simply element 120, is the hypothetical chemical element in the periodic table with symbol Ubn and atomic number 120. ''Unbinilium'' and ''Ubn'' are the temporary systematic IUPAC name and symbol, which ar ...

, 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 film Soap films are thin layers of liquid (usually water-based) surrounded by air. For example, if two soap bubbles come into contact, they merge and a thin film is created in between. Thus, foams are composed of a network of films connected by Platea ...

s meet along a Plateau border at 120

^\circ

angles.

In religion

* The

cubit The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding ...

s of the height of the Temple building (

II Chronicles The Book of Chronicles ( he, דִּבְרֵי־הַיָּמִים ) is a book in the Hebrew Bible, found as two books (1–2 Chronicles) in the Christian Old Testament. Chronicles is the final book of the Hebrew Bible, concluding the third sect ...

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 The Hebrew Bible or Tanakh (;"Tanach"
'' Jewish prayers Listed below are some Hebrew prayers and blessings that are part of Judaism that are recited by many Jews. Most prayers and blessings can be found in the Siddur, or prayer book. This article addresses Jewish liturgical blessings, which generally ...

* The number of talents of gold that the Queen of Sheba gave to Solomon in tribute (

I Kings The Book of Kings (, '' Sēfer Məlāḵīm'') is a book in the Hebrew Bible, found as two books (1–2 Kings) in the Old Testament of the Christian Bible. It concludes the Deuteronomistic history, a history of Israel also including the boo ...

10:10) * The number of princes King Darius set over his kingdom ( Daniel 6:2) * The summed weight in

shekel Shekel or sheqel ( akk, 𒅆𒅗𒇻 ''šiqlu'' or ''siqlu,'' he, שקל, plural he, שקלים or shekels, Phoenician: ) is an ancient Mesopotamian coin, usually of silver. A shekel was first a unit of weight—very roughly —and became c ...

s of the gold spoons offered by each tribal prince of Israel (Num. 7:86). * In

astrology Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...

, 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.

In sports

* The height in inches of a regulation hoop in the

National Basketball Association The National Basketball Association (NBA) is a professional basketball league in North America. The league is composed of 30 teams (29 in the United States and 1 in Canada) and is one of the major professional sports leagues in the United St ...

In other fields

120 is also: * The

medical Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care practic ...

telephone number A telephone number is a sequence of digits assigned to a landline telephone subscriber station connected to a telephone line or to a wireless electronic telephony device, such as a radio telephone or a mobile telephone, or to other devices f ...

in China * In

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...

, the telephone number to report a car breakdown on the highway. * In the US Army, a common diameter for a mortar in mm (M120). *

TT scale TT scale is a model railroading scale, whose name stands for ''table top''. Its 1:120 scale (from a common engineering scale where one inch equals ten feet) and gauge are roughly halfway between HO scale (1:87) and N scale (1:160). Its origina ...

, a scale for model trains, is 1:120. * 120 film is a

medium format film Medium format has traditionally referred to a film format in photography and the related cameras and equipment that use film. Nowadays, the term applies to film and digital cameras that record images on media larger than the used in 135 fil ...

developed by

Kodak The Eastman Kodak Company (referred to simply as Kodak ) is an American public company that produces various products related to its historic basis in analogue photography. The company is headquartered in Rochester, New York, and is incorpor ...

. * ''120'' (film), a 2008 Turkish film * The Israeli national legislature, the

Knesset The Knesset ( he, הַכְּנֶסֶת ; "gathering" or "assembly") is the unicameral legislature of Israel. As the supreme state body, the Knesset is sovereign and thus has complete control of the entirety of the Israeli government (with ...

, has 120 seats. *

China Airlines Flight 120 China Airlines Flight 120 was a regularly scheduled flight from Taiwan Taoyuan International Airport in Taoyuan County (now Taoyuan City), Taiwan to Naha Airport in Okinawa, Japan. On August 20, 2007, the Boeing 737-800 aircraft operating the f ...

References

* Wells, D. ''

The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, ...