456312734208 has 480 divisors, whose sum is σ = 1406417126400. Its totient is φ = 142121852928.

The previous prime is 456312734177. The next prime is 456312734221. The reversal of 456312734208 is 802437213654.

456312734208 is a `hidden beast` number, since 4 + 5 + 631 + 2 + 7 + 3 + 4 + 2 + 0 + 8 = 666.

It is a super-2 number, since 2×456312734208² (a number of 24 digits) contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1271065933 + ... + 1271066291.

It is an arithmetic number, because the mean of its divisors is an integer number (2930035680).

Almost surely, 2^456312734208 is an apocalyptic number.

456312734208 is a gapful number since it is divisible by the number (48) 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 456312734208, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (703208563200).

456312734208 is an abundant number, since it is smaller than the sum of its proper divisors (950104392192).

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

456312734208 is a wasteful number, since it uses less digits than its factorization.

456312734208 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 652 (or 633 counting only the distinct ones).

The product of its (nonzero) digits is 967680, while the sum is 45.

The spelling of 456312734208 in words is "four hundred fifty-six billion, three hundred twelve million, seven hundred thirty-four thousand, two hundred eight".