What are the divisors of 228?

1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228

There is a total of 12 positive divisors.
The sum of these divisors is 560.
The arithmetic mean is 46.666666666667.

8 even divisors

2, 4, 6, 12, 38, 76, 114, 228

4 odd divisors

1, 3, 19, 57

How to compute the divisors of 228?

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 228 by each of the numbers from 1 to 228 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)

228 / 1 = 228 (the remainder is 0, so 1 is a divisor of 228)
228 / 2 = 114 (the remainder is 0, so 2 is a divisor of 228)
228 / 3 = 76 (the remainder is 0, so 3 is a divisor of 228)
...
228 / 227 = 1.0044052863436 (the remainder is 1, so 227 is not a divisor of 228)
228 / 228 = 1 (the remainder is 0, so 228 is a divisor of 228)

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 228 (i.e. 15.099668870541). 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 $\frac{N}{d} = D$ )

228 / 1 = 228 (the remainder is 0, so 1 and 228 are divisors of 228)
228 / 2 = 114 (the remainder is 0, so 2 and 114 are divisors of 228)
228 / 3 = 76 (the remainder is 0, so 3 and 76 are divisors of 228)
...
228 / 14 = 16.285714285714 (the remainder is 4, so 14 is not a divisor of 228)
228 / 15 = 15.2 (the remainder is 3, so 15 is not a divisor of 228)