460688000 has 64 divisors (see below), whose sum is σ = 1145425320. Its totient is φ = 184268800.

The previous prime is 460687991. The next prime is 460688021. The reversal of 460688000 is 886064.

It can be written as a sum of positive squares in 4 ways, for example, as 88661056 + 372026944 = 9416^2 + 19288^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (32).

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 7 ways as a sum of consecutive naturals, for example, 1604 + ... + 30396.

Almost surely, 2^460688000 is an apocalyptic number.

460688000 is a gapful number since it is divisible by the number (40) 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 460688000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (572712660).

460688000 is an abundant number, since it is smaller than the sum of its proper divisors (684737320).

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

460688000 is an equidigital number, since it uses as much as digits as its factorization.

460688000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28822 (or 28800 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 32.

The square root of 460688000 is about 21463.6436794874. The cubic root of 460688000 is about 772.3289245982.

The spelling of 460688000 in words is "four hundred sixty million, six hundred eighty-eight thousand".