What are the divisors of 5018?

1, 2, 13, 26, 193, 386, 2509, 5018

There is a total of 8 positive divisors.
The sum of these divisors is 8148.
The arithmetic mean is 1018.5.

4 even divisors

2, 26, 386, 5018

4 odd divisors

1, 13, 193, 2509

How to compute the divisors of 5018?

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 5018 by each of the numbers from 1 to 5018 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)

5018 / 1 = 5018 (the remainder is 0, so 1 is a divisor of 5018)
5018 / 2 = 2509 (the remainder is 0, so 2 is a divisor of 5018)
5018 / 3 = 1672.6666666667 (the remainder is 2, so 3 is not a divisor of 5018)
...
5018 / 5017 = 1.0001993223042 (the remainder is 1, so 5017 is not a divisor of 5018)
5018 / 5018 = 1 (the remainder is 0, so 5018 is a divisor of 5018)

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 5018 (i.e. 70.837842993699). 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 $\frac{N}{d} = D$ )

5018 / 1 = 5018 (the remainder is 0, so 1 and 5018 are divisors of 5018)
5018 / 2 = 2509 (the remainder is 0, so 2 and 2509 are divisors of 5018)
5018 / 3 = 1672.6666666667 (the remainder is 2, so 3 is not a divisor of 5018)
...
5018 / 69 = 72.724637681159 (the remainder is 50, so 69 is not a divisor of 5018)
5018 / 70 = 71.685714285714 (the remainder is 48, so 70 is not a divisor of 5018)