72588 has 24 divisors (see below), whose sum is σ = 177408. Its totient is φ = 23056.

The previous prime is 72577. The next prime is 72613. The reversal of 72588 is 88527.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 72588.

It is an unprimeable number.

72588 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 7 ways as a sum of consecutive naturals, for example, 145 + ... + 407.

It is an arithmetic number, because the mean of its divisors is an integer number (7392).

2⁷²⁵⁸⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72588, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (88704).

72588 is an abundant number, since it is smaller than the sum of its proper divisors (104820).

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

72588 is a wasteful number, since it uses less digits than its factorization.

72588 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 293 (or 291 counting only the distinct ones).

The product of its digits is 4480, while the sum is 30.

The square root of 72588 is about 269.4216026973. The cubic root of 72588 is about 41.7146185714.

The spelling of 72588 in words is "seventy-two thousand, five hundred eighty-eight".