312984000 has 672 divisors, whose sum is σ = 1384621056. Its totient is φ = 68428800.

The previous prime is 312983969. The next prime is 312984019. The reversal of 312984000 is 489213.

It is a tau number, because it is divible by the number of its divisors (672).

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

It is a zygodrome in base 12.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 13607989 + ... + 13608011.

It is an arithmetic number, because the mean of its divisors is an integer number (2060448).

Almost surely, 2^312984000 is an apocalyptic number.

312984000 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 312984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (692310528).

312984000 is an abundant number, since it is smaller than the sum of its proper divisors (1071637056).

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

312984000 is an equidigital number, since it uses as much as digits as its factorization.

312984000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 72 (or 40 counting only the distinct ones).

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

The square root of 312984000 is about 17691.3538204401. The cubic root of 312984000 is about 678.9545642686.

The spelling of 312984000 in words is "three hundred twelve million, nine hundred eighty-four thousand".