83328 has 64 divisors (see below), whose sum is σ = 261120. Its totient is φ = 23040.

The previous prime is 83311. The next prime is 83339. The reversal of 83328 is 82338.

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (24).

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

It is a junction number, because it is equal to n+sod(n) for n = 83298 and 83307.

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 83328.

It is an unprimeable 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, 2673 + ... + 2703.

It is an arithmetic number, because the mean of its divisors is an integer number (4080).

2⁸³³²⁸ 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 83328, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (130560).

83328 is an abundant number, since it is smaller than the sum of its proper divisors (177792).

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

83328 is a wasteful number, since it uses less digits than its factorization.

83328 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 55 (or 43 counting only the distinct ones).

The product of its digits is 1152, while the sum is 24.

The square root of 83328 is about 288.6658968427. The cubic root of 83328 is about 43.6780913978.

Subtracting from 83328 its reverse (82338), we obtain a triangular number (990 = T₄₄).

It can be divided in two parts, 833 and 28, that added together give a triangular number (861 = T₄₁).

The spelling of 83328 in words is "eighty-three thousand, three hundred twenty-eight".