312912 has 60 divisors (see below), whose sum is σ = 914004. Its totient is φ = 99840.

The previous prime is 312899. The next prime is 312929. The reversal of 312912 is 219213.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 104976 + 207936 = 324^2 + 456^2 .

It is a hoax number, since the sum of its digits (18) 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 (18).

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

Its product of digits (108) is a multiple of the sum of its prime factors (108).

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 312912.

It is an unprimeable number.

312912 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 (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 5878 + ... + 5930.

2³¹²⁹¹² 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 312912, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (457002).

312912 is an abundant number, since it is smaller than the sum of its proper divisors (601092).

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

312912 is a wasteful number, since it uses less digits than its factorization.

312912 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 108 (or 99 counting only the distinct ones).

The product of its digits is 108, while the sum is 18.

The square root of 312912 is about 559.3853769987. The cubic root of 312912 is about 67.8902497201.

The spelling of 312912 in words is "three hundred twelve thousand, nine hundred twelve".