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 common divisor of the polynomial and its formal derivative). A positive integer "n" is square-free if and only if in the prime factorization of "n", no prime factor occurs with an exponent larger than one. Another way of stating the same is that for every prime factor "p" of "n", the prime "p" does not evenly divide "n" / "p". Also "n" is square-free if and only if in every factorization "n" = "ab", the factors "a" and "b" are coprime. An immediate result of this definition is that all prime numbers are square-free. A positive integer "n" is square-free