60 (sixty) () 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 59 and preceding 61. Being three times 20, it is called '' threescore'' in older literature ('' kopa'' in Slavic, ''Schock'' in Germanic).

In mathematics

* 60 is a

highly composite number __FORCETOC__ A highly composite number is a positive integer with more divisors than any smaller positive integer has. The related concept of largely composite number refers to a positive integer which has at least as many divisors as any smaller ...

. Because it is the sum of its unitary divisors (excluding itself), it is a

unitary perfect number A unitary perfect number is an integer which is the sum of its positive proper unitary divisors, not including the number itself (a divisor ''d'' of a number ''n'' is a unitary divisor if ''d'' and ''n''/''d'' share no common factors). Some perfect ...

, and it is an

abundant number In number theory, an abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. Th ...

with an abundance of 48. Being ten times a perfect number, it is a

semiperfect number In number theory, a semiperfect number or pseudoperfect number is a natural number ''n'' that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number. ...

. * It is the smallest number divisible by the numbers 1 to 6: there is no smaller number divisible by the numbers 1 to 5. * It is the smallest number with exactly 12 divisors. * It is one of seven integers that have more divisors than any number less than twice itself , one of six that are also lowest common multiple of a consecutive set of integers from 1, and one of six that are divisors of every highly composite number higher than itself. * It is the smallest number that is the sum of two odd primes in six ways.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, ...

'' London: Penguin Group. (1987): 109–110. * The smallest non

solvable group In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminate ...

( A₅) has order 60. Icosidodecahedron

* There are four Archimedean solids with 60 vertices: the

truncated icosahedron In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose 32 faces are two or more types of regular polygons. It is the only one of these shapes that does not contain triangles or squares. ...

, the

rhombicosidodecahedron In geometry, the rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pen ...

, the

snub dodecahedron In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces. The snub dodecahedron has 92 faces (the most ...

, and the

truncated dodecahedron In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges. Geometric relations This polyhedron can be formed from a regular dodecahedron by tr ...

. The skeletons of these polyhedra form 60-node

vertex-transitive graph In the mathematical field of graph theory, a vertex-transitive graph is a graph in which, given any two vertices and of , there is some automorphism :f : G \to G\ such that :f(v_1) = v_2.\ In other words, a graph is vertex-transitive ...

s. There are also two Archimedean solids with 60 edges: the

snub cube In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles. It has 60 edges and 24 vertices. It is a chiral polyhedron; that is, it has two distinct forms, which are mirr ...

and the

icosidodecahedron In geometry, an icosidodecahedron is a polyhedron with twenty (''icosi'') triangular faces and twelve (''dodeca'') pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 i ...

. The skeleton of the icosidodecahedron forms a 60-edge

symmetric graph In the mathematical field of graph theory, a graph is symmetric (or arc-transitive) if, given any two pairs of adjacent vertices and of , there is an automorphism :f : V(G) \rightarrow V(G) such that :f(u_1) = u_2 and f(v_1) = v_2. In oth ...

. * There are 60 one-sided hexominoes, the

polyomino A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in pop ...

es made from six squares. * In

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...

, it is the number of seconds in a minute, and the number of minutes in a degree. * In normal space, the three interior angles of an

equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each oth ...

each measure 60 degrees, adding up to 180 degrees. * Because it is divisible by the sum of its digits in decimal, it is a Harshad number. * A number system with base 60 is called

sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form ...

(the original meaning of ''sexagesimal'' is sixtieth). * It is the smallest positive integer that is written with only the smallest and the largest digit of base 2 (

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...

), base 3 ( ternary), and base 4 ( quaternary). * 60 is also the product of the side lengths of the smallest whole number

right triangle A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right a ...

: 3, 4, 5, a type of

Pythagorean triple A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A primitive Pythagorean triple is ...

In science and technology

The first

fullerene A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ...

to be discovered was

buckminsterfullerene Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a soccer ball. Each of its 60 carbon atoms is bonded ...

C₆₀, an

allotrope of carbon Carbon is capable of forming many allotropes (structurally different forms of the same element) due to its valency. Well-known forms of carbon include diamond and graphite. In recent decades, many more allotropes have been discovered and rese ...

with 60

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...

s in each

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

, arranged in a

. This ball is known as a buckyball, and looks like a

soccer ball A football (also known as football ball, soccer ball, or association football ball specifically in the United Kingdom) is the ball used in the sport of association football. The name of the ball varies according to whether the sport is called " ...

. 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 ...

neodymium Neodymium is a chemical element with the symbol Nd and atomic number 60. It is the fourth member of the lanthanide series and is considered to be one of the rare-earth metals. It is a hard, slightly malleable, silvery metal that quickly tarnishe ...

is 60, and

cobalt-60 Cobalt-60 (60Co) is a synthetic radioactive isotope of cobalt with a half-life of 5.2713 years. It is produced artificially in nuclear reactors. Deliberate industrial production depends on neutron activation of bulk samples of the monoisot ...

(⁶⁰Co) is a

radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is consi ...

isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...

cobalt Cobalt is a chemical element with the symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. The free element, p ...

. The electrical

utility frequency The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominal frequency of the oscillations of alternating current (AC) in a wide area synchronous grid transmitted from a power station to t ...

in western Japan, South Korea, Taiwan, the Philippines, the United States, and several other countries in the Americas is 60 Hz. An

exbibyte The byte is a unit of digital information that most commonly consists of eight bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a ...

(sometimes called

exabyte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable uni ...

) is 2⁶⁰

byte The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable uni ...

Cultural number systems

The

Babylonian cuneiform numerals Assyro-Chaldean Babylonian cuneiform numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. The Babylonians, who were fam ...

had a base of 60, inherited from the Sumerian and Akkadian civilizations, and possibly motivated by the large number of divisors that 60 has. The

measurement of time and of geometric angles is a legacy of the Babylonian system. The number system in the Mali Empire was based on 60, reflected in the counting system of the

Maasina Fulfulde Fula ,Laurie Bauer, 2007, ''The Linguistics Student’s Handbook'', Edinburgh also known as Fulani or Fulah (, , ; Adlam: , , ), is a Senegambian language spoken by around 30 million people as a set of various dialects in a continuum that str ...

, a variant of the Fula language spoken in contemporary

Mali Mali (; ), officially the Republic of Mali,, , ff, 𞤈𞤫𞤲𞥆𞤣𞤢𞥄𞤲𞤣𞤭 𞤃𞤢𞥄𞤤𞤭, Renndaandi Maali, italics=no, ar, جمهورية مالي, Jumhūriyyāt Mālī is a landlocked country in West Africa. Mal ...

. The Ekagi of

Western New Guinea Western New Guinea, also known as Papua, Indonesian New Guinea, or Indonesian Papua, is the western half of the Melanesian island of New Guinea which is administered by Indonesia. Since the island is alternatively named as Papua, the region ...

used base 60, and the

sexagenary cycle The sexagenary cycle, also known as the Stems-and-Branches or ganzhi ( zh, 干支, gānzhī), is a cycle of sixty terms, each corresponding to one year, thus a total of sixty years for one cycle, historically used for recording time in China and t ...

plays a role in Chinese calendar and numerology. From

Polish–Lithuanian Commonwealth The Polish–Lithuanian Commonwealth, formally known as the Kingdom of Poland and the Grand Duchy of Lithuania, and, after 1791, as the Commonwealth of Poland, was a bi- confederal state, sometimes called a federation, of Poland and Lithuania ru ...

in Slavic and Baltic languages 60 has its own name '' kopa'' ( pl, kopa, be, капа́, lt, kapa, cz, kopa, , uk, копа́), in Germanic languages: german: Schock, , , , and in la, sexagena refer to 60 = 5

dozen A dozen (commonly abbreviated doz or dz) is a grouping of twelve. The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year ...

= small gross. This quantity was used in international medieval treaties e.g. for ransom of captured

Teutonic Knights The Order of Brothers of the German House of Saint Mary in Jerusalem, commonly known as the Teutonic Order, is a Catholic religious institution founded as a military society in Acre, Kingdom of Jerusalem. It was formed to aid Christians o ...

In religion

60 occurs several times in the

Bible The Bible (from Koine Greek , , 'the books') is a collection of religious texts or scriptures that are held to be sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthologya compilation of texts ...

; for example, as the age of

Isaac Isaac; grc, Ἰσαάκ, Isaák; ar, إسحٰق/إسحاق, Isḥāq; am, ይስሐቅ is one of the three patriarchs of the Israelites and an important figure in the Abrahamic religions, including Judaism, Christianity, and Islam. He was th ...

when

Jacob Jacob (; ; ar, يَعْقُوب, Yaʿqūb; gr, Ἰακώβ, Iakṓb), later given the name Israel, is regarded as a patriarch of the Israelites and is an important figure in Abrahamic religions, such as Judaism, Christianity, and Islam. J ...

and

Esau Esau ''Ēsaû''; la, Hesau, Esau; ar, عِيسَوْ ''‘Īsaw''; meaning "hairy"Easton, M. ''Illustrated Bible Dictionary'', (, , 2006, p. 236 or "rough".Mandel, D. ''The Ultimate Who's Who in the Bible'', (.), 2007, p. 175 is the elder son o ...

were born, and the number of warriors escorting King Solomon. In the laws of kashrut of

Judaism Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...

, 60 is the proportion (60:1) of kosher to non-kosher ingredients that can render an admixture kosher post-facto. In the Quran, 60 is mentioned once: "..he should feed sixty indigent ones..", but it is mentioned many times in the Hadith, most notably Muhammad being reported to say, "..Allah, the Exalted and Glorious, created Adam in His own image with His length of sixty cubits.." In Hinduism, the 60th birthday of a man is called Sashti poorthi. A ceremony called Sashti (60) Abda (years) Poorthi (completed) in Sanskrit is conducted to felicitate this birthday. It represents a milestone in his life. There are 60 years mentioned in the historic Indian calendars.

In other fields

It is: * In

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...

, the number of seconds in a minute, and the number of minutes in an hour.Dennis Guedj, ''Numbers: The Universal Language'', transl. Lory Frankel. New York: Harry N. Abrams, Inc. Publishers (1997): 71. "60: the ace of divisibility. The more divisible a number is ... the more useful it proves in certain situations. ... Is it because 60 is highly divisible that the hour has been divided into 60 minutes, and the minute into 60 seconds? Look at the list of its twelve divisors ... Compare this with the larger number 100, which has only nine divisors." (a legacy of the Babylonian number system) * The number of feet in the standard measurement tool to evaluate an automotive launch on a

dragstrip A dragstrip is a facility for conducting automobile and motorcycle acceleration events such as drag racing. Although a quarter mile (1320 feet, 402 m) is the best known measure for a drag track, many tracks are eighth mile (201&n ...

, as the time taken to travel the first of the track. * The number of miles per hour an automobile accelerates to from rest ( 0-60) as one of the standard measurements of performance * The number of years in a

* '' 60 Minutes'', a

CBS CBS Broadcasting Inc., commonly shortened to CBS, the abbreviation of its former legal name Columbia Broadcasting System, is an American commercial broadcast television and radio network serving as the flagship property of the CBS Entertainm ...

investigative

television Television, sometimes shortened to TV, is a telecommunication medium for transmitting moving images and sound. The term can refer to a television set, or the medium of television transmission. Television is a mass medium for advertisin ...

show * ''

Sixty Minute Man "Sixty Minute Man" is a rhythm and blues (R&B) record released on Federal Records in 1951 by the Dominoes. It was written by Billy Ward and Rose Marks and was one of the first R&B hit records to cross over to become a hit on the pop chart. It ...

'' was a TV show starring Kenny Baumann * A common

speed limit Speed limits on road traffic, as used in most countries, set the legal maximum speed at which vehicles may travel on a given stretch of road. Speed limits are generally indicated on a traffic sign reflecting the maximum permitted speed - expre ...

, in miles per hour, for

freeway A controlled-access highway is a type of highway that has been designed for high-speed vehicular traffic, with all traffic flow—ingress and egress—regulated. Common English terms are freeway, motorway and expressway. Other similar terms ...

s in many

U.S. The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

states * A common

, in kilometers per hour, in urban areas in

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-eig ...

* In years of

marriage Marriage, also called matrimony or wedlock, is a culturally and often legally recognized union between people called spouses. It establishes rights and obligations between them, as well as between them and their children, and between ...

, the

diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...

wedding anniversary A wedding anniversary is the anniversary of the date a wedding took place. Couples may take the occasion to celebrate their relationship, either privately or with a larger party. Special celebrations and gifts are often given for particular an ...

* The maximum number of

marbles A marble is a small spherical object often made from glass, clay, steel, plastic, or agate. They vary in size, and most commonly are about in diameter. These toys can be used for a variety of games called ''marbles'', as well being placed in mar ...

(game pieces) in Chinese checkers * The

code for international direct dial Country calling codes or country dial-in codes are telephone number prefixes for reaching telephone subscribers in the networks of the member countries or regions of the International Telecommunication Union (ITU). The codes are defined by the ...

calls to

Malaysia Malaysia ( ; ) is a country in Southeast Asia. The federation, federal constitutional monarchy consists of States and federal territories of Malaysia, thirteen states and three federal territories, separated by the South China Sea into two r ...

* The highest attainable level in ''

World of Warcraft ''World of Warcraft'' (''WoW'') is a massively multiplayer online role-playing game (MMORPG) released in 2004 by Blizzard Entertainment. Set in the ''Warcraft'' fantasy universe, ''World of Warcraft'' takes place within the world of Azeroth ...

'' (not including the five latest expansions) * ''

Studio 60 on the Sunset Strip ''Studio 60 on the Sunset Strip'' is an American comedy-drama television series created and primarily written by Aaron Sorkin. The series was about the production of a live comedy series, similar to ''Saturday Night Live''. Produced by Warner Br ...

'' was a TV show on

NBC The National Broadcasting Company (NBC) is an American English-language commercial broadcast television and radio network. The flagship property of the NBC Entertainment division of NBCUniversal, a division of Comcast, its headquarters are l ...

(2006–07) * '' Gone in 60 Seconds'' is a movie starring

Nicolas Cage Nicolas Kim Coppola (born January 7, 1964), known professionally as Nicolas Cage, is an American actor and film producer. Born into the Coppola family, he is the recipient of various accolades, including an Academy Award, a Screen Actors Gui ...

* Miss Sixty is a women's apparel brand * The number of cards in the game Rack-O * The number of the

French department In the administrative divisions of France, the department (french: département, ) is one of the three levels of government under the national level ("territorial collectivity, territorial collectivities"), between the regions of France, admin ...

Oise Oise ( ; ; pcd, Oése) is a department in the north of France. It is named after the river Oise. Inhabitants of the department are called ''Oisiens'' () or ''Isariens'', after the Latin name for the river, Isara. It had a population of 829,41 ...

* Alpha 60 is a brain-computer in the movie ''Alphaville'' directed by Jean-Luc Godard * The age for

senior citizen Old age refers to ages nearing or surpassing the life expectancy of human beings, and is thus the end of the human life cycle. Terms and euphemisms for people at this age include old people, the elderly (worldwide usage), OAPs (British usage ...

s in some cultures

In sports

* In

darts Darts or dart-throwing is a competitive sport in which two or more players bare-handedly throw small sharp-pointed missiles known as darts at a round target known as a dartboard. Points can be scored by hitting specific marked areas of the bo ...

, 60 (treble-twenty) is the highest score that can be achieved with a single dart. *

New York Yankees The New York Yankees are an American professional baseball team based in the New York City borough of the Bronx. The Yankees compete in Major League Baseball (MLB) as a member club of the American League (AL) East division. They are one of ...

Babe Ruth George Herman "Babe" Ruth Jr. (February 6, 1895 – August 16, 1948) was an American professional baseball player whose career in Major League Baseball (MLB) spanned 22 seasons, from 1914 through 1935. Nicknamed "the Bambino" and "the Su ...

hit 60 home runs in 1927 during a 154-game season; although the record has been broken three times since then, by Roger Maris,

Mark McGwire Mark David McGwire (born October 1, 1963), nicknamed "Big Mac", is an American former professional baseball first baseman who played 16 seasons in Major League Baseball (MLB) from 1986 to 2001 for the Oakland Athletics and the St. Louis Card ...

, and Barry Bonds (with Sammy Sosa and

Aaron Judge Aaron James Judge (born April 26, 1992) is an American professional baseball outfielder for the New York Yankees of Major League Baseball (MLB). Judge was unanimously selected as the American League (AL) Rookie of the Year in 2017, and finishe ...

also exceeding that total), those records were set during a 162-game season. * In

NCAA Division II NCAA Division II (D-II) is an intermediate-level division of competition in the National Collegiate Athletic Association (NCAA). It offers an alternative to both the larger and better-funded Division I and to the scholarship-free environmen ...

, each member school may provide athletically-related financial aid in men's sports amounting to no more than the equivalent of 60 full

scholarships A scholarship is a form of financial aid awarded to students for further education. Generally, scholarships are awarded based on a set of criteria such as academic merit, diversity and inclusion, athletic skill, and financial need. Scholarsh ...

. Basketball and football are excluded from this limit by rule. * The total number of minutes in an

ice hockey Ice hockey (or simply hockey) is a team sport played on ice skates, usually on an ice skating rink with lines and markings specific to the sport. It belongs to a family of sports called hockey. In ice hockey, two opposing teams use ice h ...

game, divided into three periods. * The total number of minutes in a gridiron football game, divided into four quarters.

References

External links

* {{Integers, zero Integers

In mathematics

In science and technology

Cultural number systems

In religion

In other fields

In sports

See also

References

External links