468384000 has 576 divisors, whose sum is σ = 1928489472. Its totient is φ = 98304000.

The previous prime is 468383963. The next prime is 468384011. The reversal of 468384000 is 483864.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 11423980 + ... + 11424020.

It is an arithmetic number, because the mean of its divisors is an integer number (3348072).

Almost surely, 2^468384000 is an apocalyptic number.

468384000 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 468384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (964244736).

468384000 is an abundant number, since it is smaller than the sum of its proper divisors (1460105472).

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

468384000 is a wasteful number, since it uses less digits than its factorization.

468384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 99 (or 75 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 33.

The square root of 468384000 is about 21642.1810361156. The cubic root of 468384000 is about 776.6058965839.

The spelling of 468384000 in words is "four hundred sixty-eight million, three hundred eighty-four thousand".