What are the divisors of 2218?

1, 2, 1109, 2218

There is a total of 4 positive divisors.
The sum of these divisors is 3330.
The arithmetic mean is 832.5.

2 even divisors

2, 2218

2 odd divisors

1, 1109

How to compute the divisors of 2218?

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 2218 by each of the numbers from 1 to 2218 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)

2218 / 1 = 2218 (the remainder is 0, so 1 is a divisor of 2218)
2218 / 2 = 1109 (the remainder is 0, so 2 is a divisor of 2218)
2218 / 3 = 739.33333333333 (the remainder is 1, so 3 is not a divisor of 2218)
...
2218 / 2217 = 1.000451059991 (the remainder is 1, so 2217 is not a divisor of 2218)
2218 / 2218 = 1 (the remainder is 0, so 2218 is a divisor of 2218)

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 2218 (i.e. 47.095647357266). 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 $\frac{N}{d} = D$ )

2218 / 1 = 2218 (the remainder is 0, so 1 and 2218 are divisors of 2218)
2218 / 2 = 1109 (the remainder is 0, so 2 and 1109 are divisors of 2218)
2218 / 3 = 739.33333333333 (the remainder is 1, so 3 is not a divisor of 2218)
...
2218 / 46 = 48.217391304348 (the remainder is 10, so 46 is not a divisor of 2218)
2218 / 47 = 47.191489361702 (the remainder is 9, so 47 is not a divisor of 2218)