314516800 has 84 divisors (see below), whose sum is σ = 833494396. Its totient is φ = 116121600.

The previous prime is 314516773. The next prime is 314516819. The reversal of 314516800 is 8615413.

It can be written as a sum of positive squares in 6 ways, for example, as 70157376 + 244359424 = 8376^2 + 15632^2 .

It is a super-3 number, since 3×314516800³ (a number of 26 digits) contains 333 as substring.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 13240 + ... + 28360.

Almost surely, 2^314516800 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 314516800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (416747198).

314516800 is an abundant number, since it is smaller than the sum of its proper divisors (518977596).

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

314516800 is a wasteful number, since it uses less digits than its factorization.

314516800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 15156 (or 15141 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 28.

The square root of 314516800 is about 17734.6215070974. The cubic root of 314516800 is about 680.0611248398.

The spelling of 314516800 in words is "three hundred fourteen million, five hundred sixteen thousand, eight hundred".