312864 has 24 divisors (see below), whose sum is σ = 821520. Its totient is φ = 104256.

The previous prime is 312863. The next prime is 312887. The reversal of 312864 is 468213.

It is a happy number.

312864 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (24).

It is a hoax number, since the sum of its digits (24) coincides with the sum of the digits of its distinct prime factors.

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 d-powerful number, because it can be written as 3¹¹ + 1 + 8³ + 2¹⁷ + 6² + 4⁶ .

It is one of the 548 Lynch-Bell numbers.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 312864.

It is not an unprimeable number, because it can be changed into a prime (312863) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1534 + ... + 1725.

It is an arithmetic number, because the mean of its divisors is an integer number (34230).

2³¹²⁸⁶⁴ is an apocalyptic number.

It is an amenable number.

312864 is an abundant number, since it is smaller than the sum of its proper divisors (508656).

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

312864 is a wasteful number, since it uses less digits than its factorization.

312864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3272 (or 3264 counting only the distinct ones).

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

The square root of 312864 is about 559.3424711212. The cubic root of 312864 is about 67.8867781385.

It can be divided in two parts, 312 and 864, that added together give a triangular number (1176 = T₄₈).

The spelling of 312864 in words is "three hundred twelve thousand, eight hundred sixty-four".