82320 has 80 divisors (see below), whose sum is σ = 297600. Its totient is φ = 18816.

The previous prime is 82307. The next prime is 82339. The reversal of 82320 is 2328.

It is a tau number, because it is divible by the number of its divisors (80).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nialpdrome in base 14.

It is a zygodrome in base 14.

It is a self number, because there is not a number n which added to its sum of digits gives 82320.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 82320.

It is an unprimeable number.

82320 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 15 ways as a sum of consecutive naturals, for example, 11757 + ... + 11763.

It is an arithmetic number, because the mean of its divisors is an integer number (3720).

2⁸²³²⁰ is an apocalyptic number.

82320 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 82320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148800).

82320 is an abundant number, since it is smaller than the sum of its proper divisors (215280).

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

82320 is a wasteful number, since it uses less digits than its factorization.

82320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 37 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 82320 is about 286.9146214469. The cubic root of 82320 is about 43.5012550834.

Adding to 82320 its reverse (2328), we get a palindrome (84648).

The spelling of 82320 in words is "eighty-two thousand, three hundred twenty".