# 64 (number)

 ← 63 64 65 →
Cardinal sixty-four
Ordinal 64th
(sixty-fourth)
Factorization 26
Divisors 1, 2, 4, 8, 16, 32, 64
Roman numeral LXIV
Binary 10000002
Ternary 21013
Quaternary 10004
Quinary 2245
Senary 1446
Octal 1008
Duodecimal 5412
Vigesimal 3420
Base 36 1S36

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

## 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. 64 is also the first whole number that is both a perfect square and a perfect cube.

Since it is possible to find sequences of 64 consecutive integers such that each inner 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.

64 is the index of Graham's number in the rapidly growing sequence $3\uparrow\uparrow\uparrow\uparrow 3$,$3\uparrow^{3 \uparrow\uparrow\uparrow\uparrow 3}3$,...

## In science

### Astronomy

• The Saros number of the solar eclipse series which began on -832 April 11 and ended on 430 May. The duration of Saros series 64 was 1262.1 years, and it contained 71 solar eclipses.
• The Saros number of the lunar eclipse series which began on -801 August 9 and ended on 714 February. The duration of Saros series 64 was 1514.5 years, and it contained 85 lunar eclipses.

## In other fields

A chessboard has 64 squares

Sixty-four is: