What are the divisors of 2238?

1, 2, 3, 6, 373, 746, 1119, 2238

There is a total of 8 positive divisors.
The sum of these divisors is 4488.
The arithmetic mean is 561.

4 even divisors

2, 6, 746, 2238

4 odd divisors

1, 3, 373, 1119

How to compute the divisors of 2238?

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 2238 by each of the numbers from 1 to 2238 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)

2238 / 1 = 2238 (the remainder is 0, so 1 is a divisor of 2238)
2238 / 2 = 1119 (the remainder is 0, so 2 is a divisor of 2238)
2238 / 3 = 746 (the remainder is 0, so 3 is a divisor of 2238)
...
2238 / 2237 = 1.0004470272687 (the remainder is 1, so 2237 is not a divisor of 2238)
2238 / 2238 = 1 (the remainder is 0, so 2238 is a divisor of 2238)

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 2238 (i.e. 47.307504690059). 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 $\frac{N}{d} = D$ )

2238 / 1 = 2238 (the remainder is 0, so 1 and 2238 are divisors of 2238)
2238 / 2 = 1119 (the remainder is 0, so 2 and 1119 are divisors of 2238)
2238 / 3 = 746 (the remainder is 0, so 3 and 746 are divisors of 2238)
...
2238 / 46 = 48.652173913043 (the remainder is 30, so 46 is not a divisor of 2238)
2238 / 47 = 47.617021276596 (the remainder is 29, so 47 is not a divisor of 2238)