65664 has 64 divisors (see below), whose sum is σ = 204000. Its totient is φ = 20736.

The previous prime is 65657. The next prime is 65677. The reversal of 65664 is 46656.

65664 is a `hidden beast` number, since 656 + 6 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (27).

Its product of digits (4320) is a multiple of the sum of its prime divisors (24).

It is a nialpdrome in base 12.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 65664.

It is an unprimeable number.

65664 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 3447 + ... + 3465.

2⁶⁵⁶⁶⁴ is an apocalyptic number.

65664 is a gapful number since it is divisible by the number (64) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 65664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102000).

65664 is an abundant number, since it is smaller than the sum of its proper divisors (138336).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

65664 is a wasteful number, since it uses less digits than its factorization.

65664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 24 counting only the distinct ones).

The product of its digits is 4320, while the sum is 27.

The square root of 65664 is about 256.2498780488. The cubic root of 65664 is about 40.3437048816.

It can be divided in two parts, 65 and 664, that added together give a 6-th power (729 = 3⁶).

The spelling of 65664 in words is "sixty-five thousand, six hundred sixty-four".