312064000 has 192 divisors, whose sum is σ = 827910720. Its totient is φ = 117145600.

The previous prime is 312063967. The next prime is 312064001. The reversal of 312064000 is 460213.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (312064001) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 5887974 + ... + 5888026.

It is an arithmetic number, because the mean of its divisors is an integer number (4312035).

Almost surely, 2^312064000 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 312064000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (413955360).

312064000 is an abundant number, since it is smaller than the sum of its proper divisors (515846720).

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

312064000 is an equidigital number, since it uses as much as digits as its factorization.

312064000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 113 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 16.

The square root of 312064000 is about 17665.3332830151. Note that the first 3 decimals coincide. The cubic root of 312064000 is about 678.2886609733.

The spelling of 312064000 in words is "three hundred twelve million, sixty-four thousand".