What are the divisors of 8244?

1, 2, 3, 4, 6, 9, 12, 18, 36, 229, 458, 687, 916, 1374, 2061, 2748, 4122, 8244

There is a total of 18 positive divisors.
The sum of these divisors is 20930.
The arithmetic mean is 1162.7777777778.

12 even divisors

2, 4, 6, 12, 18, 36, 458, 916, 1374, 2748, 4122, 8244

6 odd divisors

1, 3, 9, 229, 687, 2061

How to compute the divisors of 8244?

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 8244 by each of the numbers from 1 to 8244 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)

8244 / 1 = 8244 (the remainder is 0, so 1 is a divisor of 8244)
8244 / 2 = 4122 (the remainder is 0, so 2 is a divisor of 8244)
8244 / 3 = 2748 (the remainder is 0, so 3 is a divisor of 8244)
...
8244 / 8243 = 1.0001213150552 (the remainder is 1, so 8243 is not a divisor of 8244)
8244 / 8244 = 1 (the remainder is 0, so 8244 is a divisor of 8244)

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 8244 (i.e. 90.796475702529). 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 $\frac{N}{d} = D$ )

8244 / 1 = 8244 (the remainder is 0, so 1 and 8244 are divisors of 8244)
8244 / 2 = 4122 (the remainder is 0, so 2 and 4122 are divisors of 8244)
8244 / 3 = 2748 (the remainder is 0, so 3 and 2748 are divisors of 8244)
...
8244 / 89 = 92.629213483146 (the remainder is 56, so 89 is not a divisor of 8244)
8244 / 90 = 91.6 (the remainder is 54, so 90 is not a divisor of 8244)