What are the divisors of 5188?

1, 2, 4, 1297, 2594, 5188

There is a total of 6 positive divisors.
The sum of these divisors is 9086.
The arithmetic mean is 1514.3333333333.

4 even divisors

2, 4, 2594, 5188

2 odd divisors

1, 1297

How to compute the divisors of 5188?

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 5188 by each of the numbers from 1 to 5188 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)

5188 / 1 = 5188 (the remainder is 0, so 1 is a divisor of 5188)
5188 / 2 = 2594 (the remainder is 0, so 2 is a divisor of 5188)
5188 / 3 = 1729.3333333333 (the remainder is 1, so 3 is not a divisor of 5188)
...
5188 / 5187 = 1.0001927896665 (the remainder is 1, so 5187 is not a divisor of 5188)
5188 / 5188 = 1 (the remainder is 0, so 5188 is a divisor of 5188)

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 5188 (i.e. 72.027772421476). 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 $\frac{N}{d} = D$ )

5188 / 1 = 5188 (the remainder is 0, so 1 and 5188 are divisors of 5188)
5188 / 2 = 2594 (the remainder is 0, so 2 and 2594 are divisors of 5188)
5188 / 3 = 1729.3333333333 (the remainder is 1, so 3 is not a divisor of 5188)
...
5188 / 71 = 73.070422535211 (the remainder is 5, so 71 is not a divisor of 5188)
5188 / 72 = 72.055555555556 (the remainder is 4, so 72 is not a divisor of 5188)