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
Squaring the square and "R"'s smallest edge square is adjacent to smaller squares not on the edge. Therefore, the smallest square "s" in "R" is surrounded by "larger", and therefore "higher", cubes on all four sides. Hence the upper face of the cube on "s" is divided into a perfect squared square by the cubes which rest on it. Let "s" be the smallest square in this dissection. The sequence of squares "s", "s", ... is infinite and the corresponding cubes are infinite in number. This contradicts our original supposition. If a 4-dimensional hypercube could be perfectly hypercubed then its 'faces' would be