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60

Please do not rely on any information it contains.

60 is an integer, the smallest positive integer divisible by all integers from 1 to 6 (see A003418).

Membership in core sequences

 Even numbers ..., 52, 54, 56, 58, 60, 62, 64, 66, ... A005843 Composite numbers ..., 56, 57, 58, 60, 62, 63, 64, 65, ... A002808 Abundant numbers ..., 48, 54, 56, 60, 66, 70, 72, 78, ... A005101 Binary partition numbers ..., 26, 36, 46, 60, 74, 94, 114, 140, ... A000123 Number of ways of dissecting a polygoninto ${\displaystyle n}$ quadrilaterals ..., 2, 5, 16, 60, 261, 1243, 6257, ... A005036 Orders of non-cyclic simple groups 60, 168, 360, 504, 660, 1092, 2448, ... A001034

Sequences pertaining to 60

 Multiples of 60 0, 60, 120, 180, 240, 300, 360, ... A169823 Divisors of 60 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 A018266

Partitions of 60

There are 966467 partitions of 60.

The Goldbach representations of 60 are: 7 + 53 = 13 + 47 = 17 + 43 = 19 + 41 = 23 + 37 = 29 + 31.

PLACEHOLDER

PLACEHOLDER

PLACEHOLDER

Representation of 60 in various bases

 Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Representation 111100 2020 330 220 140 114 74 66 60 55 50 48 44 40 3C 39 36 33 30

As you can see from the table above, 60 is a Harshad number in every base from binary to vigesimal, except bases 8, 14, 18. It is also a Harshad number in bases 21, 25, 26, 28, 29, 30, 31, 41, 46, 49, 51, 55, 56, 57, 58, 59, and trivially in base 60 and above.

 ${\displaystyle -1}$ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 1729