82800 has 90 divisors (see below), whose sum is σ = 299832. Its totient is φ = 21120.

The previous prime is 82799. The next prime is 82811. The reversal of 82800 is 828.

It is a tau number, because it is divible by the number of its divisors (90).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

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 17 ways as a sum of consecutive naturals, for example, 3589 + ... + 3611.

2⁸²⁸⁰⁰ is an apocalyptic number.

82800 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149916).

82800 is an abundant number, since it is smaller than the sum of its proper divisors (217032).

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

82800 is a wasteful number, since it uses less digits than its factorization.

82800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 47 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 18.

The square root of 82800 is about 287.7498913988. The cubic root of 82800 is about 43.5856418227.

Adding to 82800 its product of nonzero digits (128), we get a palindrome (82928).

Multiplying 82800 by its reverse (828), we get a square (68558400 = 8280²).

82800 divided by its reverse (828) gives a square (100 = 10²).

The spelling of 82800 in words is "eighty-two thousand, eight hundred".