103584 has 48 divisors (see below), whose sum is σ = 296352. Its totient is φ = 31488.

The previous prime is 103583. The next prime is 103591. The reversal of 103584 is 485301.

It is a tau number, because it is divible by the number of its divisors (48).

It is a super-3 number, since 3×103584³ = 3334258660442112, which contains 333 as substring.

It is an Ulam number.

It is a self number, because there is not a number n which added to its sum of digits gives 103584.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 103584.

It is not an unprimeable number, because it can be changed into a prime (103583) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1207 + ... + 1289.

It is an arithmetic number, because the mean of its divisors is an integer number (6174).

2¹⁰³⁵⁸⁴ 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 103584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148176).

103584 is an abundant number, since it is smaller than the sum of its proper divisors (192768).

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

103584 is a wasteful number, since it uses less digits than its factorization.

103584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 109 (or 101 counting only the distinct ones).

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

The square root of 103584 is about 321.8446830383. The cubic root of 103584 is about 46.9639077068.

Adding to 103584 its reverse (485301), we get a palindrome (588885).

The spelling of 103584 in words is "one hundred three thousand, five hundred eighty-four".