• 64 can be written using four 4's:

• There are 64 permutations of {1,2,3,4,5} which contain at least 3 collinear elements:

64 has 7 divisors (see below), whose sum is σ = 127. Its totient is φ = 32.

The previous prime is 61. The next prime is 67. The reversal of 64 is 46.

64 = T_{5} + T_{6} +
T_{7}.

The square root of 64 is 8.

The cubic root of 64 is 4.

It is a perfect power (a square, a cube, a 6-th power), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (2!)^{6}.

64 is nontrivially palindromic in base 7 and base 15.

64 is an esthetic number in base 3, base 7 and base 12, because in such bases its adjacent digits differ by 1.

It is an interprime number because it is at equal distance from previous prime (61) and next prime (67).

It is an ABA number since it can be written as A⋅B^{A}, here for A=4, B=2.

It is a cake number, because a cake can be divided into 64 parts by 7 planar cuts.

It is a Duffinian number.

64 is an undulating number in base 7.

Its product of digits (24) is a multiple of the sum of its prime divisors (2).

64 is a nontrivial repdigit in base 15.

It is a plaindrome in base 5, base 6, base 11, base 13, base 14 and base 15.

It is a nialpdrome in base 2, base 4, base 8, base 9, base 10, base 12, base 15 and base 16.

It is a zygodrome in base 15.

It is a self number, because there is not a number *n* which added to its sum of digits gives 64.

It is an upside-down number.

In principle, a polygon with 64 sides can be constructed with ruler and compass.

It is an impolite number, since it cannot be written as a nontrivial sum of consecutive naturals.

64 is the 8-th square number.

64 is the 7-th centered triangular number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 64

64 is a deficient number, since it is larger than the sum of its proper divisors (63).

64 is an equidigital number, since it uses as much as digits as its factorization.

64 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 12 (or 2 counting only the distinct ones).

The product of its digits is 24, while the sum is 10.

Adding to 64 its product of digits (24), we get a palindrome (88).

The spelling of 64 in words is "sixty-four", and thus it is an aban number and an eban number.

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