456960000 has 480 divisors, whose sum is σ = 1842160320. Its totient is φ = 98304000.

The previous prime is 456959977. The next prime is 456960001. The reversal of 456960000 is 69654.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a self number, because there is not a number n which added to its sum of digits gives 456960000.

It is not an unprimeable number, because it can be changed into a prime (456960001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 26879992 + ... + 26880008.

It is an arithmetic number, because the mean of its divisors is an integer number (3837834).

Almost surely, 2^456960000 is an apocalyptic number.

456960000 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 456960000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (921080160).

456960000 is an abundant number, since it is smaller than the sum of its proper divisors (1385200320).

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

456960000 is an equidigital number, since it uses as much as digits as its factorization.

456960000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 69 (or 34 counting only the distinct ones).

The product of its (nonzero) digits is 6480, while the sum is 30.

The square root of 456960000 is about 21376.6227454198. The cubic root of 456960000 is about 770.2399881617.

The spelling of 456960000 in words is "four hundred fifty-six million, nine hundred sixty thousand".