64 (number) 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. In base 10, no integer added up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ("n")) = 2"n". 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,… Sixty-four is: 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube
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