49584 has 20 divisors (see below), whose sum is σ = 128216. Its totient is φ = 16512.

The previous prime is 49559. The next prime is 49597. The reversal of 49584 is 48594.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 49584.

It is an unprimeable number.

49584 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 3 ways as a sum of consecutive naturals, for example, 469 + ... + 564.

49584 is a Friedman number, since it can be written as 48*(9+4^5), using all its digits and the basic arithmetic operations.

2⁴⁹⁵⁸⁴ is an apocalyptic number.

It is an amenable number.

49584 is an abundant number, since it is smaller than the sum of its proper divisors (78632).

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 (64108).

49584 is a wasteful number, since it uses less digits than its factorization.

49584 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1044 (or 1038 counting only the distinct ones).

The product of its digits is 5760, while the sum is 30.

The square root of 49584 is about 222.6746505555. The cubic root of 49584 is about 36.7378598430.

Subtracting from 49584 its reverse (48594), we obtain a triangular number (990 = T₄₄).

The spelling of 49584 in words is "forty-nine thousand, five hundred eighty-four".