314688000 has 320 divisors, whose sum is σ = 1149033600. Its totient is φ = 75776000.

The previous prime is 314687999. The next prime is 314688043. The reversal of 314688000 is 886413.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (320).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 2111926 + ... + 2112074.

It is an arithmetic number, because the mean of its divisors is an integer number (3590730).

Almost surely, 2^314688000 is an apocalyptic number.

314688000 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 314688000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (574516800).

314688000 is an abundant number, since it is smaller than the sum of its proper divisors (834345600).

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

314688000 is a wasteful number, since it uses less digits than its factorization.

314688000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 196 (or 170 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 30.

The square root of 314688000 is about 17739.4475674977. The cubic root of 314688000 is about 680.1844943453.

The spelling of 314688000 in words is "three hundred fourteen million, six hundred eighty-eight thousand".