312984 has 96 divisors (see below), whose sum is σ = 1048320. Its totient is φ = 85536.

The previous prime is 312979. The next prime is 312989. The reversal of 312984 is 489213.

It is an interprime number because it is at equal distance from previous prime (312979) and next prime (312989).

It is a Harshad number since it is a multiple of its sum of digits (27).

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

It is one of the 548 Lynch-Bell numbers.

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 312984.

It is not an unprimeable number, because it can be changed into a prime (312989) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 13597 + ... + 13619.

It is an arithmetic number, because the mean of its divisors is an integer number (10920).

2³¹²⁹⁸⁴ 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 312984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (524160).

312984 is an abundant number, since it is smaller than the sum of its proper divisors (735336).

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

312984 is a wasteful number, since it uses less digits than its factorization.

312984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 35 counting only the distinct ones).

The product of its digits is 1728, while the sum is 27.

The square root of 312984 is about 559.4497296451. The cubic root of 312984 is about 67.8954564269.

It can be divided in two parts, 312 and 984, that added together give a 4-th power (1296 = 6⁴).

The spelling of 312984 in words is "three hundred twelve thousand, nine hundred eighty-four".