86304 has 48 divisors (see below), whose sum is σ = 241920. Its totient is φ = 26880.

The previous prime is 86297. The next prime is 86311. The reversal of 86304 is 40368.

86304 = 37² + 38² + ... + 67².

It is an interprime number because it is at equal distance from previous prime (86297) and next prime (86311).

It is a tau number, because it is divible by the number of its divisors (48).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 86304.

It is an unprimeable number.

86304 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 7 ways as a sum of consecutive naturals, for example, 2769 + ... + 2799.

It is an arithmetic number, because the mean of its divisors is an integer number (5040).

2⁸⁶³⁰⁴ 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 86304, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (120960).

86304 is an abundant number, since it is smaller than the sum of its proper divisors (155616).

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

86304 is a wasteful number, since it uses less digits than its factorization.

86304 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 86304 is about 293.7754244317. The cubic root of 86304 is about 44.1919984424.

The spelling of 86304 in words is "eighty-six thousand, three hundred four".