459984 has 60 divisors (see below), whose sum is σ = 1395744. Its totient is φ = 127872.

The previous prime is 459961. The next prime is 460013. The reversal of 459984 is 489954.

It is a congruent number.

It is an unprimeable number.

459984 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 12414 + ... + 12450.

2⁴⁵⁹⁹⁸⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 459984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (697872).

459984 is an abundant number, since it is smaller than the sum of its proper divisors (935760).

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

459984 is a wasteful number, since it uses less digits than its factorization.

459984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 92 (or 49 counting only the distinct ones).

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

The square root of 459984 is about 678.2212028535. The cubic root of 459984 is about 77.1935312754.

The spelling of 459984 in words is "four hundred fifty-nine thousand, nine hundred eighty-four".