459984000 has 384 divisors, whose sum is σ = 1791054720. Its totient is φ = 102297600.

The previous prime is 459983987. The next prime is 459984013. The reversal of 459984000 is 489954.

It is an interprime number because it is at equal distance from previous prime (459983987) and next prime (459984013).

It is a tau number, because it is divible by the number of its divisors (384).

It is a self number, because there is not a number n which added to its sum of digits gives 459984000.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 12431982 + ... + 12432018.

It is an arithmetic number, because the mean of its divisors is an integer number (4664205).

Almost surely, 2^459984000 is an apocalyptic number.

459984000 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 459984000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (895527360).

459984000 is an abundant number, since it is smaller than the sum of its proper divisors (1331070720).

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

459984000 is an equidigital number, since it uses as much as digits as its factorization.

459984000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 113 (or 54 counting only the distinct ones).

The product of its (nonzero) digits is 51840, while the sum is 39.

The square root of 459984000 is about 21447.2375843604. The cubic root of 459984000 is about 771.9353127540.

The spelling of 459984000 in words is "four hundred fifty-nine million, nine hundred eighty-four thousand".