85632 has 32 divisors (see below), whose sum is σ = 228480. Its totient is φ = 28416.

The previous prime is 85627. The next prime is 85639. The reversal of 85632 is 23658.

It is a tau number, because it is divible by the number of its divisors (32).

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 Harshad number since it is a multiple of its sum of digits (24).

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

Its product of digits (1440) is a multiple of the sum of its prime factors (240).

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 85632.

It is not an unprimeable number, because it can be changed into a prime (85639) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 273 + ... + 495.

It is an arithmetic number, because the mean of its divisors is an integer number (7140).

2⁸⁵⁶³² 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 85632, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (114240).

85632 is an abundant number, since it is smaller than the sum of its proper divisors (142848).

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

85632 is a wasteful number, since it uses less digits than its factorization.

85632 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 240 (or 228 counting only the distinct ones).

The product of its digits is 1440, while the sum is 24.

The square root of 85632 is about 292.6294585308. The cubic root of 85632 is about 44.0770001571.

It can be divided in two parts, 856 and 32, that added together give a palindrome (888).

The spelling of 85632 in words is "eighty-five thousand, six hundred thirty-two".