313664000 has 240 divisors, whose sum is σ = 876138120. Its totient is φ = 111820800.

The previous prime is 313663993. The next prime is 313664009. The reversal of 313664000 is 466313.

313664000 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 12 ways, for example, as 97456384 + 216207616 = 9872^2 + 14704^2 .

It is not an unprimeable number, because it can be changed into a prime (313664009) 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, 10815986 + ... + 10816014.

Almost surely, 2^313664000 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 313664000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (438069060).

313664000 is an abundant number, since it is smaller than the sum of its proper divisors (562474120).

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

313664000 is an equidigital number, since it uses as much as digits as its factorization.

313664000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 23.

The square root of 313664000 is about 17710.5618205635. The cubic root of 313664000 is about 679.4459154197.

The spelling of 313664000 in words is "three hundred thirteen million, six hundred sixty-four thousand".