What are the divisors of 5218?

1, 2, 2609, 5218

There is a total of 4 positive divisors.
The sum of these divisors is 7830.
The arithmetic mean is 1957.5.

2 even divisors

2, 5218

2 odd divisors

1, 2609

How to compute the divisors of 5218?

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 5218 by each of the numbers from 1 to 5218 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)

5218 / 1 = 5218 (the remainder is 0, so 1 is a divisor of 5218)
5218 / 2 = 2609 (the remainder is 0, so 2 is a divisor of 5218)
5218 / 3 = 1739.3333333333 (the remainder is 1, so 3 is not a divisor of 5218)
...
5218 / 5217 = 1.0001916810427 (the remainder is 1, so 5217 is not a divisor of 5218)
5218 / 5218 = 1 (the remainder is 0, so 5218 is a divisor of 5218)

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 5218 (i.e. 72.235725233433). 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 $\frac{N}{d} = D$ )

5218 / 1 = 5218 (the remainder is 0, so 1 and 5218 are divisors of 5218)
5218 / 2 = 2609 (the remainder is 0, so 2 and 2609 are divisors of 5218)
5218 / 3 = 1739.3333333333 (the remainder is 1, so 3 is not a divisor of 5218)
...
5218 / 71 = 73.492957746479 (the remainder is 35, so 71 is not a divisor of 5218)
5218 / 72 = 72.472222222222 (the remainder is 34, so 72 is not a divisor of 5218)