|Factorization||22· 3 · 5|
|Divisors||1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60|
Sixty is a composite number with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it also a highly composite number. Because 60 is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is also an excessive number with an abundance of 48. Being ten times a perfect number, 60 is a semiperfect number.
Sixty is the smallest number divisible by the numbers 1 to 6. (There is no smaller number divisible by the numbers 1 to 5). 60 is the smallest number with exactly 12 divisors. It is one of only 7 integers that have more divisors than any number twice itself (sequence A072938 in OEIS), and is one of only 6 that are also lowest common multiple of a consecutive set of integers from 1, and one of the 6 that are divisors of every highly composite number higher than itself.(sequence A106037 in OEIS)
Sixty is the sum of a pair of twin primes (29 + 31), as well as the sum of four consecutive primes (11 + 13 + 17 + 19). It is adjacent to two prime numbers (59,61). It is also the smallest number which is the sum of two odd primes in 6 ways.
There are four Archimedean solids with 60 vertices: the truncated icosahedron, the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron. The skeletons of these polyhedra form 60-node vertex-transitive graphs. There are also two Archimedean solids with 60 edges: the snub cube and the icosidodecahedron. The skeleton of the icosidodecahedron forms a 60-edge symmetric graph.
In geometry, 60 is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the 3 interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees.
Because 60 is divisible by the sum of its digits in base 10, it is a Harshad number.
A number system with base 60 is called sexagesimal (the original meaning of sexagesimal is sixtieth).
In science and technology
The first fullerene to be discovered was buckminsterfullerene C60 – an allotrope of carbon with 60 atoms in each molecule, arranged in a truncated icosahedron. This ball is known as a buckyball, and looks like a soccer ball.
Cultural number systems
The Babylonian number system had a base of sixty, inherited from the Sumerian and Akkadian civilizations, and possibly motivated by the large number of divisors which 60 has. The sexagesimal measurement of time and of geometric angles is a legacy of the Babylonian system.
The number system in the Mali Empire was also based on sixty (this is reflected in the counting system of the Maasina Fulfulde, a variant of the Fula language spoken in contemporary Mali). The Ekagi of Western New Guinea have also used base 60, and the sexagenary cycle also plays a role in Chinese calendar and numerology.
In the Koran, the number 60 is mentioned once: "..he should feed sixty indigent ones..", yet 60 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 other fields
- In time, the number of seconds in a minute, and the number of minutes in an hour. (a legacy of the Babylonian number system)
- The number of feet in the standard measurement tool to evaluate an automotive launch on a dragstrip. It's the time that it took to travel the first 60 feet (18 m) 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 total number of years in a Sexagenary cycle
- 60 Minutes, a CBS investigative television show
- Sixty Minute Man was a TV show starring Kenny Baumann
- The number of the European route E60 from Brest, France, to Constanţa, Romania
- Municipal Okrug 60, name of Posadsky Municipal Okrug of Petrogradsky District of St. Petersburg, Russia until April 2009
- A common speed limit, in miles per hour, for freeways in many U.S. states
- A common speed limit, in kilometers per hour, in urban areas in Russia
- In years of marriage, the diamond wedding anniversary
- The maximum number of marbles (game pieces) in Chinese checkers
- The code for international direct dial calls to Malaysia
- The highest obtainable level on World of Warcraft (not including the 3 latest expansions)
- Studio 60 on the Sunset Strip was a TV show on NBC (2006–07)
- Gone in 60 Seconds is a movie starring Nicolas Cage
- Miss Sixty is a women's apparel brand
- The total number of cards in the game Rack-O
- The number of the French department Oise
- Alpha 60 is a brain-computer in the movie Alphaville directed by Jean-Luc Godard
- The age for senior citizen in some cultures
- In darts, 60 (treble-twenty) is the highest score which can be achieved with a single dart.
- New York Yankees Babe Ruth hit 60 home runs in 1927 during a 154-game season; although the record was broken three times since then (Roger Maris, Mark McGwire, and Barry Bonds) those records were set during a 162-game season
|Look up sixty in Wiktionary, the free dictionary.|
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 109–110.
- La Fontane, Jean sybil (2004). The Interpretation of Ritual: Essays in Honour of A.I. Richards. Routledge. p. 320.
- Bowers, Nancy (1977). "Kapauku numeration: Reckoning, racism, scholarship, and Melanesian counting systems". Journal of the Polynesian Society 86 (1): 105–116
- Biblegateway Genesis 25:26
- Biblegateway Song of Solomon 3:7
- Talmud, Tractate Chullin 98b ; Shulchan Aruch, Yoreh Deah 98.
- Koran, Al-Mujadala,4
- 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."