What are the divisors of 8228?

1, 2, 4, 11, 17, 22, 34, 44, 68, 121, 187, 242, 374, 484, 748, 2057, 4114, 8228

There is a total of 18 positive divisors.
The sum of these divisors is 16758.
The arithmetic mean is 931.

12 even divisors

2, 4, 22, 34, 44, 68, 242, 374, 484, 748, 4114, 8228

6 odd divisors

1, 11, 17, 121, 187, 2057

How to compute the divisors of 8228?

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 8228 by each of the numbers from 1 to 8228 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)

8228 / 1 = 8228 (the remainder is 0, so 1 is a divisor of 8228)
8228 / 2 = 4114 (the remainder is 0, so 2 is a divisor of 8228)
8228 / 3 = 2742.6666666667 (the remainder is 2, so 3 is not a divisor of 8228)
...
8228 / 8227 = 1.0001215509906 (the remainder is 1, so 8227 is not a divisor of 8228)
8228 / 8228 = 1 (the remainder is 0, so 8228 is a divisor of 8228)

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 8228 (i.e. 90.708323763589). 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 $\frac{N}{d} = D$ )

8228 / 1 = 8228 (the remainder is 0, so 1 and 8228 are divisors of 8228)
8228 / 2 = 4114 (the remainder is 0, so 2 and 4114 are divisors of 8228)
8228 / 3 = 2742.6666666667 (the remainder is 2, so 3 is not a divisor of 8228)
...
8228 / 89 = 92.449438202247 (the remainder is 40, so 89 is not a divisor of 8228)
8228 / 90 = 91.422222222222 (the remainder is 38, so 90 is not a divisor of 8228)