460814400 has 168 divisors, whose sum is σ = 1679996640. Its totient is φ = 122872320.

The previous prime is 460814399. The next prime is 460814441. The reversal of 460814400 is 4418064.

460814400 is a `hidden beast` number, since 4 + 608 + 14 + 40 + 0 = 666.

It is a super-2 number, since 2×460814400² = 424699822494720000, which contains 22 as substring.

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

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 37867 + ... + 48533.

It is an arithmetic number, because the mean of its divisors is an integer number (9999980).

Almost surely, 2^460814400 is an apocalyptic number.

460814400 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 460814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (839998320).

460814400 is an abundant number, since it is smaller than the sum of its proper divisors (1219182240).

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

460814400 is a wasteful number, since it uses less digits than its factorization.

460814400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10698 (or 10677 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 460814400 is about 21466.5879915743. The cubic root of 460814400 is about 772.3995533456.

The spelling of 460814400 in words is "four hundred sixty million, eight hundred fourteen thousand, four hundred".