314294400 has 288 divisors, whose sum is σ = 1282507200. Its totient is φ = 71792640.

The previous prime is 314294389. The next prime is 314294401. The reversal of 314294400 is 4492413.

314294400 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (288).

It is not an unprimeable number, because it can be changed into a prime (314294401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 200821 + ... + 202379.

It is an arithmetic number, because the mean of its divisors is an integer number (4453150).

Almost surely, 2^314294400 is an apocalyptic number.

314294400 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 314294400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (641253600).

314294400 is an abundant number, since it is smaller than the sum of its proper divisors (968212800).

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

314294400 is a wasteful number, since it uses less digits than its factorization.

314294400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1596 (or 1576 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 27.

The square root of 314294400 is about 17728.3501770469. The cubic root of 314294400 is about 679.9007929089.

The spelling of 314294400 in words is "three hundred fourteen million, two hundred ninety-four thousand, four hundred".