82400 has 36 divisors (see below), whose sum is σ = 203112. Its totient is φ = 32640.

The previous prime is 82393. The next prime is 82421. The reversal of 82400 is 428.

It is a plaindrome in base 11.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 749 + ... + 851.

It is an arithmetic number, because the mean of its divisors is an integer number (5642).

2⁸²⁴⁰⁰ is an apocalyptic number.

82400 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 82400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (101556).

82400 is an abundant number, since it is smaller than the sum of its proper divisors (120712).

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

82400 is a wasteful number, since it uses less digits than its factorization.

82400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 123 (or 110 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 82400 is about 287.0540018881. The cubic root of 82400 is about 43.5153422783.

Adding to 82400 its reverse (428), we get a palindrome (82828).

The spelling of 82400 in words is "eighty-two thousand, four hundred".