64 (number) 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. 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
Square number must also divide ; if fails to divide , then is definitely not square. Repeating the divisions of the previous sentence, one concludes that every prime must divide a given perfect square an even number of times (including possibly 0 times). Thus, the number is a square number if and only if, in its canonical representation, all exponents are even. Squarity testing can be used as alternative way in factorization of large numbers. Instead of testing for divisibility, test for squarity: for given and some number , if is the square of an integer then divides . (This is an