456896000 has 240 divisors, whose sum is σ = 1273512240. Its totient is φ = 163328000.

The previous prime is 456895997. The next prime is 456896047. The reversal of 456896000 is 698654.

It is a congruent number.

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, 7743971 + ... + 7744029.

It is an arithmetic number, because the mean of its divisors is an integer number (5306301).

Almost surely, 2^456896000 is an apocalyptic number.

456896000 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 456896000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (636756120).

456896000 is an abundant number, since it is smaller than the sum of its proper divisors (816616240).

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

456896000 is an equidigital number, since it uses as much as digits as its factorization.

456896000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 114 (or 77 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 38.

The square root of 456896000 is about 21375.1257306244. The cubic root of 456896000 is about 770.2040275665.

The spelling of 456896000 in words is "four hundred fifty-six million, eight hundred ninety-six thousand".