What are the divisors of 8226?

1, 2, 3, 6, 9, 18, 457, 914, 1371, 2742, 4113, 8226

There is a total of 12 positive divisors.
The sum of these divisors is 17862.
The arithmetic mean is 1488.5.

6 even divisors

2, 6, 18, 914, 2742, 8226

6 odd divisors

1, 3, 9, 457, 1371, 4113

How to compute the divisors of 8226?

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 8226 by each of the numbers from 1 to 8226 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)

8226 / 1 = 8226 (the remainder is 0, so 1 is a divisor of 8226)
8226 / 2 = 4113 (the remainder is 0, so 2 is a divisor of 8226)
8226 / 3 = 2742 (the remainder is 0, so 3 is a divisor of 8226)
...
8226 / 8225 = 1.0001215805471 (the remainder is 1, so 8225 is not a divisor of 8226)
8226 / 8226 = 1 (the remainder is 0, so 8226 is a divisor of 8226)

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 8226 (i.e. 90.697298746986). 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 $\frac{N}{d} = D$ )

8226 / 1 = 8226 (the remainder is 0, so 1 and 8226 are divisors of 8226)
8226 / 2 = 4113 (the remainder is 0, so 2 and 4113 are divisors of 8226)
8226 / 3 = 2742 (the remainder is 0, so 3 and 2742 are divisors of 8226)
...
8226 / 89 = 92.426966292135 (the remainder is 38, so 89 is not a divisor of 8226)
8226 / 90 = 91.4 (the remainder is 36, so 90 is not a divisor of 8226)