460812172800 has 960 divisors, whose sum is σ = 1902073688064. Its totient is φ = 95905382400.

The previous prime is 460812172789. The next prime is 460812172801. The reversal of 460812172800 is 8271218064.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (960).

It is a super-3 number, since 3×460812172800³ (a number of 36 digits) contains 333 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (460812172801) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 141655974 + ... + 141659226.

Almost surely, 2^460812172800 is an apocalyptic number.

460812172800 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 460812172800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (951036844032).

460812172800 is an abundant number, since it is smaller than the sum of its proper divisors (1441261515264).

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

460812172800 is a wasteful number, since it uses less digits than its factorization.

460812172800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3339 (or 3318 counting only the distinct ones).

The product of its (nonzero) digits is 43008, while the sum is 39.

The spelling of 460812172800 in words is "four hundred sixty billion, eight hundred twelve million, one hundred seventy-two thousand, eight hundred".