85752 has 32 divisors (see below), whose sum is σ = 238800. Its totient is φ = 28512.

The previous prime is 85751. The next prime is 85781. The reversal of 85752 is 25758.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 85752.

It is not an unprimeable number, because it can be changed into a prime (85751) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 18 + ... + 414.

2⁸⁵⁷⁵² 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 85752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (119400).

85752 is an abundant number, since it is smaller than the sum of its proper divisors (153048).

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

85752 is a wasteful number, since it uses less digits than its factorization.

85752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 412 (or 402 counting only the distinct ones).

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

The square root of 85752 is about 292.8344242059. The cubic root of 85752 is about 44.0975795793.

It can be divided in two parts, 857 and 52, that added together give a palindrome (909).

The spelling of 85752 in words is "eighty-five thousand, seven hundred fifty-two".