What are the divisors of 5118?

1, 2, 3, 6, 853, 1706, 2559, 5118

There is a total of 8 positive divisors.
The sum of these divisors is 10248.
The arithmetic mean is 1281.

4 even divisors

2, 6, 1706, 5118

4 odd divisors

1, 3, 853, 2559

How to compute the divisors of 5118?

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 5118 by each of the numbers from 1 to 5118 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)

5118 / 1 = 5118 (the remainder is 0, so 1 is a divisor of 5118)
5118 / 2 = 2559 (the remainder is 0, so 2 is a divisor of 5118)
5118 / 3 = 1706 (the remainder is 0, so 3 is a divisor of 5118)
...
5118 / 5117 = 1.000195427008 (the remainder is 1, so 5117 is not a divisor of 5118)
5118 / 5118 = 1 (the remainder is 0, so 5118 is a divisor of 5118)

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 5118 (i.e. 71.54019849008). 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 $\frac{N}{d} = D$ )

5118 / 1 = 5118 (the remainder is 0, so 1 and 5118 are divisors of 5118)
5118 / 2 = 2559 (the remainder is 0, so 2 and 2559 are divisors of 5118)
5118 / 3 = 1706 (the remainder is 0, so 3 and 1706 are divisors of 5118)
...
5118 / 70 = 73.114285714286 (the remainder is 8, so 70 is not a divisor of 5118)
5118 / 71 = 72.084507042254 (the remainder is 6, so 71 is not a divisor of 5118)