314512400 has 60 divisors (see below), whose sum is σ = 757364100. Its totient is φ = 125514240.

The previous prime is 314512399. The next prime is 314512403. The reversal of 314512400 is 4215413.

It can be written as a sum of positive squares in 6 ways, for example, as 123298816 + 191213584 = 11104^2 + 13828^2 .

It is a super-3 number, since 3×314512400³ (a number of 26 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (314512403) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 283046 + ... + 284154.

It is an arithmetic number, because the mean of its divisors is an integer number (12622735).

Almost surely, 2^314512400 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 314512400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (378682050).

314512400 is an abundant number, since it is smaller than the sum of its proper divisors (442851700).

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

314512400 is a wasteful number, since it uses less digits than its factorization.

314512400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1836 (or 1825 counting only the distinct ones).

The product of its (nonzero) digits is 480, while the sum is 20.

The square root of 314512400 is about 17734.4974555244. The cubic root of 314512400 is about 680.0579535382.

Adding to 314512400 its reverse (4215413), we get a palindrome (318727813).

The spelling of 314512400 in words is "three hundred fourteen million, five hundred twelve thousand, four hundred".