314344800 has 756 divisors, whose sum is σ = 1460086236. Its totient is φ = 65318400.

The previous prime is 314344799. The next prime is 314344813. The reversal of 314344800 is 8443413.

314344800 is a `hidden beast` number, since 314 + 344 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (756).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 125 ways as a sum of consecutive naturals, for example, 28576795 + ... + 28576805.

It is an arithmetic number, because the mean of its divisors is an integer number (1931331).

Almost surely, 2^314344800 is an apocalyptic number.

314344800 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 314344800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (730043118).

314344800 is an abundant number, since it is smaller than the sum of its proper divisors (1145741436).

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

314344800 is a wasteful number, since it uses less digits than its factorization.

314344800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 63 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 314344800 is about 17729.7715721326. The cubic root of 314344800 is about 679.9371337499.

The spelling of 314344800 in words is "three hundred fourteen million, three hundred forty-four thousand, eight hundred".