# 64 (number)

Short description: Natural number
 ← 63 64 65 →
Cardinalsixty-four
Ordinal64th
(sixty-fourth)
Factorization26
Divisors1, 2, 4, 8, 16, 32, 64
Greek numeralΞΔ´
Roman numeralLXIV
Binary10000002
Ternary21013
Quaternary10004
Quinary2245
Senary1446
Octal1008
Duodecimal5412
Vigesimal3420
Base 361S36

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[1] and a centered triangular number.[2] 64 is also the first whole number (greater than 1) 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.[3]

In base 10, no integer added up to its own digits yields 64, hence it is a self number.[4]

64 is a superperfect number—a number such that σ(σ(n)) = 2n.[5]

64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑3↑↑↑↑3 3,…

## In other fields

A chessboard has 64 squares.

Sixty-four is:

• Up to the year 1957, the Indian currency Rupee had 64 paise. Likewise, the Pakistani Rupee also had 64 paise up to 1961.
• In chess or draughts, the total number of black (dark) and white (light) squares on the 8 by 8 game board
• The total number of gems in a standard Bejeweled game board
• 64 was the name of a former Russian chess magazine
• The code for international direct dial calls to New Zealand (+64)
• The subject of the Beatles song "When I'm Sixty-Four"
• The registry of the U.S. Navy's aircraft carrier USS Constellation (CV-64)
• The number of braille characters in the old 6-dot system
• The maximum number of strokes in any Chinese character
• Number of hexagrams in the I Ching
• Number of demons in the Dictionnaire Infernal
• Slang term referring to a 1964 Chevrolet Impala, often configured as a lowrider, a popular subject among early-1990s gangsta rap
• The number of classical arts listed in many Indian scriptures. They include: singing, dancing, painting, poetry, playing cards, making arguments, making flower garlands, etc.
• The number of the French department Pyrénées-Atlantiques
• The number of crayons in the popular Crayola 64 pack
• Number of codons in the RNA codon table under genetic code
• Number of golden disks in the myth of the Tower of Hanoi
• A number referring to Tiananmen Square protests of 1989 (Chinese: 六四事件; literally: 'Six Four Incident') in Chinese
• "64" is the title of a song by the hip-hop group Mellowhype from their album BlackenedWhite
• Number of shares in a ship or boat under British Registry owing to its divisibility by 1, 2, 4, 6, 8, 16, 32
• 64 Zoo Lane, a British animated children's TV series