72564 has 12 divisors (see below), whose sum is σ = 169344. Its totient is φ = 24184.

The previous prime is 72559. The next prime is 72577. The reversal of 72564 is 46527.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (12).

It is a Smith number, since the sum of its digits (24) coincides with the sum of the digits of its prime factors.

It is a plaindrome in base 15.

It is a congruent number.

It is an unprimeable number.

72564 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3012 + ... + 3035.

It is an arithmetic number, because the mean of its divisors is an integer number (14112).

2⁷²⁵⁶⁴ is an apocalyptic number.

It is an amenable number.

72564 is an abundant number, since it is smaller than the sum of its proper divisors (96780).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (84672).

72564 is a wasteful number, since it uses less digits than its factorization.

72564 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 6054 (or 6052 counting only the distinct ones).

The product of its digits is 1680, while the sum is 24.

The square root of 72564 is about 269.3770591569. The cubic root of 72564 is about 41.7100206525.

It can be divided in two parts, 7256 and 4, that added together give a triangular number (7260 = T₁₂₀).

The spelling of 72564 in words is "seventy-two thousand, five hundred sixty-four".