13584 has 20 divisors (see below), whose sum is σ = 35216. Its totient is φ = 4512.

The previous prime is 13577. The next prime is 13591. The reversal of 13584 is 48531.

13584 is nontrivially palindromic in base 5 and base 11.

It is an interprime number because it is at equal distance from previous prime (13577) and next prime (13591).

It is a self number, because there is not a number n which added to its sum of digits gives 13584.

It is an unprimeable number.

13584 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 (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 94 + ... + 189.

It is an amenable number.

13584 is an abundant number, since it is smaller than the sum of its proper divisors (21632).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17608).

13584 is a wasteful number, since it uses less digits than its factorization.

13584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 294 (or 288 counting only the distinct ones).

The product of its digits is 480, while the sum is 21.

The square root of 13584 is about 116.5504182747. The cubic root of 13584 is about 23.8602995128.

The spelling of 13584 in words is "thirteen thousand, five hundred eighty-four".