85584 has 20 divisors (see below), whose sum is σ = 221216. Its totient is φ = 28512.

The previous prime is 85577. The next prime is 85597. The reversal of 85584 is 48558.

It is a Smith number, since the sum of its digits (30) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 844 + ... + 939.

2⁸⁵⁵⁸⁴ is an apocalyptic number.

It is an amenable number.

85584 is an abundant number, since it is smaller than the sum of its proper divisors (135632).

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 (110608).

85584 is a wasteful number, since it uses less digits than its factorization.

85584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1794 (or 1788 counting only the distinct ones).

The product of its digits is 6400, while the sum is 30.

The square root of 85584 is about 292.5474320516. The cubic root of 85584 is about 44.0687630049.

It can be divided in two parts, 855 and 84, that added together give a palindrome (939).

The spelling of 85584 in words is "eighty-five thousand, five hundred eighty-four".