460680315076800 has 4032 divisors, whose sum is σ = 2124242428672000. Its totient is φ = 94020872601600.

The previous prime is 460680315076757. The next prime is 460680315076847. The reversal of 460680315076800 is 8670513086064.

460680315076800 is a `hidden beast` number, since 46 + 0 + 6 + 8 + 0 + 31 + 507 + 68 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (4032).

It is a hoax number, since the sum of its digits (54) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a polite number, since it can be written in 575 ways as a sum of consecutive naturals, for example, 501284346741 + ... + 501284347659.

Almost surely, 2^{460680315076800} is an apocalyptic number.

460680315076800 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 460680315076800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1062121214336000).

460680315076800 is an abundant number, since it is smaller than the sum of its proper divisors (1663562113595200).

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

460680315076800 is a wasteful number, since it uses less digits than its factorization.

460680315076800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1229 (or 1197 counting only the distinct ones).

The product of its (nonzero) digits is 5806080, while the sum is 54.

The spelling of 460680315076800 in words is "four hundred sixty trillion, six hundred eighty billion, three hundred fifteen million, seventy-six thousand, eight hundred".