72585 has 12 divisors (see below), whose sum is σ = 125892. Its totient is φ = 38688.

The previous prime is 72577. The next prime is 72613. The reversal of 72585 is 58527.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 35721 + 36864 = 189^2 + 192^2 .

It is not a de Polignac number, because 72585 - 2³ = 72577 is a prime.

It is an alternating number because its digits alternate between odd and even.

72585 is a lucky number.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 762 + ... + 851.

It is an arithmetic number, because the mean of its divisors is an integer number (10491).

2⁷²⁵⁸⁵ is an apocalyptic number.

It is an amenable number.

72585 is a deficient number, since it is larger than the sum of its proper divisors (53307).

72585 is a wasteful number, since it uses less digits than its factorization.

72585 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1624 (or 1621 counting only the distinct ones).

The product of its digits is 2800, while the sum is 27.

The square root of 72585 is about 269.4160351575. The cubic root of 72585 is about 41.7140438869.

The spelling of 72585 in words is "seventy-two thousand, five hundred eighty-five".