311328 has 72 divisors (see below), whose sum is σ = 943488. Its totient is φ = 97152.

The previous prime is 311323. The next prime is 311329. The reversal of 311328 is 823113.

It is a tau number, because it is divible by the number of its divisors (72).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is a self number, because there is not a number n which added to its sum of digits gives 311328.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 311328.

It is not an unprimeable number, because it can be changed into a prime (311323) by changing a digit.

311328 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 6601 + ... + 6647.

It is an arithmetic number, because the mean of its divisors is an integer number (13104).

2³¹¹³²⁸ 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 311328, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (471744).

311328 is an abundant number, since it is smaller than the sum of its proper divisors (632160).

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

311328 is a wasteful number, since it uses less digits than its factorization.

311328 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 86 (or 75 counting only the distinct ones).

The product of its digits is 144, while the sum is 18.

The square root of 311328 is about 557.9677410030. The cubic root of 311328 is about 67.7754995402.

The spelling of 311328 in words is "three hundred eleven thousand, three hundred twenty-eight".