64 (number)

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64 (sixty-four) is the natural number following 63 and preceding 65.

Cardinal 64
sixty-four
Ordinal 64th
sixty-fourth
Numeral system  
Factorization 2^6\,\!
Divisors 1, 2, 4, 8, 16, 32, 64
Roman numeral LXIV
Binary 1000000
Hexadecimal 40
Octal 100

Contents

[edit] In mathematics

Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number.

Since it is possible to find sequences of 64 consecutive integers such that each inner member member shares a factor with either the first or the last member, 64 is an Erdős–Woods number.

In base 10, no integer added up to its own digits yields 64, hence it is a self number.

64 is a superperfect number - a number such that σ(σ(n))=2n.

[edit] In science

[edit] Astronomy

[edit] In other fields

Sixty-four is:

  • The amount of crayons in the popular Crayola 64 pack

[edit] Historical years

64 A.D., 64 B.C., 1964, 2064, etc.

[edit] See also