314432000 has 160 divisors (see below), whose sum is σ = 833049360. Its totient is φ = 118374400.

The previous prime is 314431991. The next prime is 314432009. The reversal of 314432000 is 234413.

The cubic root of 314432000 is 680.

It is a perfect power (a cube), and thus also a powerful number.

It is an interprime number because it is at equal distance from previous prime (314431991) and next prime (314432009).

It can be written as a sum of positive squares in 8 ways, for example, as 16386304 + 298045696 = 4048^2 + 17264^2 .

It is a tau number, because it is divible by the number of its divisors (160).

It is a Harshad number since it is a multiple of its sum of digits (17).

It is a self number, because there is not a number n which added to its sum of digits gives 314432000.

It is not an unprimeable number, because it can be changed into a prime (314432009) by changing a digit.

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 15 ways as a sum of consecutive naturals, for example, 18495992 + ... + 18496008.

Almost surely, 2^314432000 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 314432000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (416524680).

314432000 is an abundant number, since it is smaller than the sum of its proper divisors (518617360).

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

314432000 is an frugal number, since it uses more digits than its factorization.

314432000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 84 (or 24 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 17.

The square root of 314432000 is about 17732.2305421512.

Adding to 314432000 its reverse (234413), we get a palindrome (314666413).

The spelling of 314432000 in words is "three hundred fourteen million, four hundred thirty-two thousand".