What are the divisors of 5584?

1, 2, 4, 8, 16, 349, 698, 1396, 2792, 5584

There is a total of 10 positive divisors.
The sum of these divisors is 10850.
The arithmetic mean is 1085.

8 even divisors

2, 4, 8, 16, 698, 1396, 2792, 5584

2 odd divisors

1, 349

How to compute the divisors of 5584?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5584 by each of the numbers from 1 to 5584 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5584 / 1 = 5584 (the remainder is 0, so 1 is a divisor of 5584)
5584 / 2 = 2792 (the remainder is 0, so 2 is a divisor of 5584)
5584 / 3 = 1861.3333333333 (the remainder is 1, so 3 is not a divisor of 5584)
...
5584 / 5583 = 1.0001791151711 (the remainder is 1, so 5583 is not a divisor of 5584)
5584 / 5584 = 1 (the remainder is 0, so 5584 is a divisor of 5584)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5584 (i.e. 74.726166769078). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5584 / 1 = 5584 (the remainder is 0, so 1 and 5584 are divisors of 5584)
5584 / 2 = 2792 (the remainder is 0, so 2 and 2792 are divisors of 5584)
5584 / 3 = 1861.3333333333 (the remainder is 1, so 3 is not a divisor of 5584)
...
5584 / 73 = 76.493150684932 (the remainder is 36, so 73 is not a divisor of 5584)
5584 / 74 = 75.459459459459 (the remainder is 34, so 74 is not a divisor of 5584)