460829952000 has 2304 divisors, whose sum is σ = 2039113440000. Its totient is φ = 102187008000.

The previous prime is 460829951969. The next prime is 460829952041. The reversal of 460829952000 is 259928064.

460829952000 is a `hidden beast` number, since 46 + 0 + 82 + 9 + 9 + 520 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2304).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 15890687986 + ... + 15890688014.

It is an arithmetic number, because the mean of its divisors is an integer number (885031875).

Almost surely, 2^460829952000 is an apocalyptic number.

460829952000 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 460829952000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1019556720000).

460829952000 is an abundant number, since it is smaller than the sum of its proper divisors (1578283488000).

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

460829952000 is a wasteful number, since it uses less digits than its factorization.

460829952000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 116 (or 69 counting only the distinct ones).

The product of its (nonzero) digits is 311040, while the sum is 45.

The spelling of 460829952000 in words is "four hundred sixty billion, eight hundred twenty-nine million, nine hundred fifty-two thousand".