What are the divisors of 5588?

1, 2, 4, 11, 22, 44, 127, 254, 508, 1397, 2794, 5588

There is a total of 12 positive divisors.
The sum of these divisors is 10752.
The arithmetic mean is 896.

8 even divisors

2, 4, 22, 44, 254, 508, 2794, 5588

4 odd divisors

1, 11, 127, 1397

How to compute the divisors of 5588?

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 5588 by each of the numbers from 1 to 5588 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)

5588 / 1 = 5588 (the remainder is 0, so 1 is a divisor of 5588)
5588 / 2 = 2794 (the remainder is 0, so 2 is a divisor of 5588)
5588 / 3 = 1862.6666666667 (the remainder is 2, so 3 is not a divisor of 5588)
...
5588 / 5587 = 1.000178986934 (the remainder is 1, so 5587 is not a divisor of 5588)
5588 / 5588 = 1 (the remainder is 0, so 5588 is a divisor of 5588)

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 5588 (i.e. 74.752926364123). 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 $\frac{N}{d} = D$ )

5588 / 1 = 5588 (the remainder is 0, so 1 and 5588 are divisors of 5588)
5588 / 2 = 2794 (the remainder is 0, so 2 and 2794 are divisors of 5588)
5588 / 3 = 1862.6666666667 (the remainder is 2, so 3 is not a divisor of 5588)
...
5588 / 73 = 76.547945205479 (the remainder is 40, so 73 is not a divisor of 5588)
5588 / 74 = 75.513513513514 (the remainder is 38, so 74 is not a divisor of 5588)