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60 (number)

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60 (sixty) (en-us-sixty.ogg Listen ) is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.

60
Cardinalsixty
Ordinal60th
(sixtieth)
Numeral systemsexagesimal
Factorization 2^2 \cdot 3 \cdot 5
Divisors1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Roman numeralLX
Binary1111002
Octal748
Duodecimal5012
Hexadecimal3C16

Contents

[edit] In mathematics

Sixty is a composite number with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 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. Being ten times a perfect number, 60 is a semiperfect number.

60 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.

This number 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).

The smallest non-abelian simple group has order 60.

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.

A number system with base-sixty is called the sexagesimal (original meaning of sexagesimal is sixtieth).

[edit] In science

Buckminsterfullerene C60 has 60 carbon atoms in each molecule

The first fullerene to be discovered was buckminsterfullerene C60 - an allotrope of carbon with 60 atoms in each molecule. This ball is known as a Bucky ball, and looks like a soccer ball.

[edit] Cultural number systems

The Babylonian number system had a base of sixty. 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).[1] The sexagenary cycle plays a role in Chinese calendar and numerology. Because 60 is divisible by the sum of its digits in base 10, it is a Harshad number. In German: das Schock and in Latin: sexagena equals 60 = 5 dozen = 1/2 small gross. This quantity was used in international medieval treaties e.g. for ransom of captured Teutonic Knights.

[edit] In religion

  • Judaism
    • In the laws of kashrut, the proportion (60:1) of kosher to non-kosher ingredients which can render an admixture kosher post-facto. (Talmud, Tractate Chullin 98b ; Shulchan Aruch, Yoreh Deah 98)
    • In the Bedtime Shema, the number of strong men (giborim) said to surround King Solomon's bed.

[edit] In other fields

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

Sixty is:

[edit] In sports

[edit] Historical years

60 A.D., 60 B.C., 1960, 2060, etc.

[edit] References

  1. ^ La Fontane, Jean sybil (2004). The Interpretation of Ritual: Essays in Honour of A.I. Richards. Routledge. pp. 320. 
  2. ^ 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."

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