51584 has 32 divisors (see below), whose sum is σ = 114240. Its totient is φ = 23040.

The previous prime is 51581. The next prime is 51593. The reversal of 51584 is 48515.

It is a tau number, because it is divible by the number of its divisors (32).

It is a nialpdrome in base 16.

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 51584.

It is not an unprimeable number, because it can be changed into a prime (51581) by changing a digit.

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, 1649 + ... + 1679.

It is an arithmetic number, because the mean of its divisors is an integer number (3570).

2⁵¹⁵⁸⁴ 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 51584, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (57120).

51584 is an abundant number, since it is smaller than the sum of its proper divisors (62656).

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

51584 is a wasteful number, since it uses less digits than its factorization.

51584 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 58 (or 46 counting only the distinct ones).

The product of its digits is 800, while the sum is 23.

The square root of 51584 is about 227.1211130653. The cubic root of 51584 is about 37.2253113283.

The spelling of 51584 in words is "fifty-one thousand, five hundred eighty-four".