82752 has 28 divisors (see below), whose sum is σ = 219456. Its totient is φ = 27520.

The previous prime is 82729. The next prime is 82757. The reversal of 82752 is 25728.

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

It is a plaindrome in base 14.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82757) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 24 + ... + 407.

2⁸²⁷⁵² 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 82752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (109728).

82752 is an abundant number, since it is smaller than the sum of its proper divisors (136704).

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

82752 is a wasteful number, since it uses less digits than its factorization.

82752 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 446 (or 436 counting only the distinct ones).

The product of its digits is 1120, while the sum is 24.

The square root of 82752 is about 287.6664735418. Note that the first 3 decimals coincide. The cubic root of 82752 is about 43.5772178484.

Subtracting from 82752 its sum of digits (24), we obtain a palindrome (82728).

The spelling of 82752 in words is "eighty-two thousand, seven hundred fifty-two".