459360 has 144 divisors (see below), whose sum is σ = 1769040. Its totient is φ = 107520.

The previous prime is 459353. The next prime is 459373. The reversal of 459360 is 63954.

459360 = 63² + 64² + ... + 117².

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-2 number, since 2×459360² = 422023219200, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

459360 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 15826 + ... + 15854.

It is an arithmetic number, because the mean of its divisors is an integer number (12285).

2⁴⁵⁹³⁶⁰ is an apocalyptic number.

459360 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 459360, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (884520).

459360 is an abundant number, since it is smaller than the sum of its proper divisors (1309680).

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

459360 is a wasteful number, since it uses less digits than its factorization.

459360 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 50 counting only the distinct ones).

The product of its (nonzero) digits is 3240, while the sum is 27.

The square root of 459360 is about 677.7610198293. The cubic root of 459360 is about 77.1586093641.

The spelling of 459360 in words is "four hundred fifty-nine thousand, three hundred sixty".