314928000 has 320 divisors, whose sum is σ = 1174464720. Its totient is φ = 83980800.

The previous prime is 314927993. The next prime is 314928007. The reversal of 314928000 is 829413.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is an interprime number because it is at equal distance from previous prime (314927993) and next prime (314928007).

It is a tau number, because it is divible by the number of its divisors (320).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (314928007) by changing a digit.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 62985598 + ... + 62985602.

Almost surely, 2^314928000 is an apocalyptic number.

314928000 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 314928000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (587232360).

314928000 is an abundant number, since it is smaller than the sum of its proper divisors (859536720).

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

314928000 is an frugal number, since it uses more digits than its factorization.

314928000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 56 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 314928000 is about 17746.2108631674. The cubic root of 314928000 is about 680.3573669432.

The spelling of 314928000 in words is "three hundred fourteen million, nine hundred twenty-eight thousand".