456115968000 has 1536 divisors, whose sum is σ = 2104733030400. Its totient is φ = 94666752000.

The previous prime is 456115967971. The next prime is 456115968017. The reversal of 456115968000 is 869511654.

456115968000 is a `hidden beast` number, since 4 + 56 + 1 + 1 + 596 + 8 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1536).

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 pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 532223572 + ... + 532224428.

It is an arithmetic number, because the mean of its divisors is an integer number (1370268900).

Almost surely, 2^456115968000 is an apocalyptic number.

456115968000 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 456115968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1052366515200).

456115968000 is an abundant number, since it is smaller than the sum of its proper divisors (1648617062400).

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

456115968000 is a wasteful number, since it uses less digits than its factorization.

456115968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 921 (or 885 counting only the distinct ones).

The product of its (nonzero) digits is 259200, while the sum is 45.

The spelling of 456115968000 in words is "four hundred fifty-six billion, one hundred fifteen million, nine hundred sixty-eight thousand".