82368 has 84 divisors (see below), whose sum is σ = 277368. Its totient is φ = 23040.

The previous prime is 82361. The next prime is 82373. The reversal of 82368 is 86328.

It is a Cunningham number, because it is equal to 287²-1.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82361) by changing a digit.

82368 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 11 ways as a sum of consecutive naturals, for example, 6330 + ... + 6342.

It is an arithmetic number, because the mean of its divisors is an integer number (3302).

2⁸²³⁶⁸ is an apocalyptic number.

82368 is a gapful number since it is divisible by the number (88) 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 82368, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138684).

82368 is an abundant number, since it is smaller than the sum of its proper divisors (195000).

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

82368 is a wasteful number, since it uses less digits than its factorization.

82368 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 42 (or 29 counting only the distinct ones).

The product of its digits is 2304, while the sum is 27.

The square root of 82368 is about 286.9982578344. The cubic root of 82368 is about 43.5097084950.

The spelling of 82368 in words is "eighty-two thousand, three hundred sixty-eight".