456312156800 has 192 divisors, whose sum is σ = 1155972497400. Its totient is φ = 177986969600.

The previous prime is 456312156791. The next prime is 456312156823. The reversal of 456312156800 is 8651213654.

It can be written as a sum of positive squares in 12 ways, for example, as 389206290496 + 67105866304 = 623864^2 + 259048^2 .

It is a Harshad number since it is a multiple of its sum of digits (41).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 220546166 + ... + 220548234.

Almost surely, 2^456312156800 is an apocalyptic number.

456312156800 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 456312156800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (577986248700).

456312156800 is an abundant number, since it is smaller than the sum of its proper divisors (699660340600).

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

456312156800 is an frugal number, since it uses more digits than its factorization.

456312156800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2216 (or 2117 counting only the distinct ones).

The product of its (nonzero) digits is 172800, while the sum is 41.

The spelling of 456312156800 in words is "four hundred fifty-six billion, three hundred twelve million, one hundred fifty-six thousand, eight hundred".