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Concept
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).
60 is a highly composite number. Because it is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is an abundant number with an abundance of 48. Being ten times a perfect number, it is a semiperfect number.
60 is a Twin-prime sum of the fifth pair of twin-primes, 29 + 31.
It is the smallest number divisible by the numbers 1 to 6: there is no smaller number divisible by the numbers 1 to 5 since any number divisible by 2 and 3 must also be divisible by 6.
It is the smallest number with exactly 12 divisors. Having 12 as one of those divisors, 60 is also a refactorable number.
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.
The smallest nonsolvable group (A5) has order 60.
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 decimal, it is a Harshad number.
A number system with base 60 is called sexagesimal (the original meaning of sexagesimal is sixtieth).
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