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-free integer (that is a integer such that is divisible by the square of every prime factor) and a square-free integer, which are coprime. The square-free factor, called the "square-free part" of the number, is the largest square-free divisor of that is coprime with . The square-free part of an integer may be smaller than the largest square-free divisor. Any arbitrary positive integer can be represented in a unique way as the product of a square and a square-free integer : In this factorization, is the largest divisor of " such that is a divisor of . In summary, there are three