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60 (number)

## Summary

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

 ← 59 60 61 →
Cardinalsixty
Ordinal60th
(sixtieth)
Factorization22 × 3 × 5
Divisors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Greek numeralΞ´
Roman numeralLX
Binary1111002
Ternary20203
Octal748
Duodecimal5012

## In mathematics

60 is a highly composite number.[1] Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number,[2] and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect 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 (sequence A072938 in the OEIS), 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.(sequence A106037 in the OEIS)

It is the smallest number that is the sum of two odd primes in six ways.[3]

The smallest non-solvable group (A5) has order 60.

The icosidodecahedron has 60 edges, all equivalent.

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.

There are 60 one-sided hexominoes, the polyominoes made from six squares.

In geometry, 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 each measure 60 degrees, adding up to 180 degrees.

Because it 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).

It is the smallest positive integer that is written with only the smallest and the largest digit of base 2 (binary), base 3 (ternary) and base 4 (quaternary).

60 is also the product of the side lengths of the smallest whole number right triangle: 3, 4, 5, a type of Pythagorean triple.[4]

## In science and technology

Buckminsterfullerene C60 has 60 carbon atoms in each molecule, arranged in a truncated icosahedron.

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.

The atomic number of neodymium is 60, and cobalt-60 (60Co) is a radioactive isotope of cobalt.

The electrical utility frequency in western Japan, South Korea, Taiwan, the Philippines, Saudi Arabia, the United States, and several other countries in the Americas is 60 Hz.

An exbibyte (sometimes called exabyte) is 260 bytes.

## Cultural number systems

Babylonian cuneiform numerals

The Babylonian cuneiform numerals 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 sexagesimal 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, a variant of the Fula language spoken in contemporary Mali.[5] The Ekagi of Western New Guinea used base 60,[6] and the sexagenary cycle plays a role in Chinese calendar and numerology.

From Polish–Lithuanian Commonwealth in Slavic and Baltic languages 60 has its own name kopa (Polish: kopa, Belarusian: капа́, Lithuanian: kapa, Czech: kopa, Russian: копа, Ukrainian: копа́), in Germanic languages: German: Schock, Danish: skok, Dutch: schok, Swedish: Skock, Norwegian: Skokk and in Latin: sexagena refer to 60 = 5 dozen = 1/2 small gross. This quantity was used in international medieval treaties e.g. for ransom of captured Teutonic Knights.

## In religion

60 occurs several times in the Bible; for example, as the age of Isaac when Jacob and Esau were born,[7] and the number of warriors escorting King Solomon.[8]

In the laws of kashrut of Judaism, 60 is the proportion (60:1) of kosher to non-kosher ingredients that can render an admixture kosher post-facto.[9]

In the Quran, 60 is mentioned once: "..he should feed sixty indigent ones..",[10] 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.."[11]

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

There are 60 seconds in a minute, and 60 minutes in an hour

It is:

## In sports

• In darts, 60 (treble-twenty) is the highest score that 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 has been broken three times since then, by Roger Maris, Mark McGwire, and Barry Bonds (with Sammy Sosa also exceeding that total), those records were set during a 162-game season.
• In NCAA Division II, each member school may provide athletically-related financial aid in men's sports amounting to no more than the equivalent of 60 full scholarships. Basketball and football are excluded from this limit by rule.

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 109–110.
4. ^ Sloane, N. J. A. (ed.). "Sequence A063011 (Ordered products of the sides of primitive Pythagorean triangles)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ La Fontane, Jean sybil (2004). The Interpretation of Ritual: Essays in Honour of A.I. Richards. Routledge. p. 320.
6. ^ Bowers, Nancy (1977). "Kapauku numeration: Reckoning, racism, scholarship, and Melanesian counting systems" (PDF). Journal of the Polynesian Society. 86 (1): 105–116. Archived from the original (PDF) on March 5, 2009.
7. ^ Biblegateway Genesis 25:26
8. ^ Biblegateway Song of Solomon 3:7
9. ^ Talmud, Tractate Chullin 98b ; Shulchan Aruch, Yoreh Deah 98.
10. ^ "Koran, Al-Mujadala,4". Archived from the original on 2011-03-10. Retrieved 2011-02-16.
11. ^ "40. The Book Pertaining to Paradise, Its Description, Its Bounties and Its Intimates (Kitab Al-Jannat wa Sifat Naimiha wa Ahliha) - Sahih Muslim - 0 - 6809".
12. ^ 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."