What are the divisors of 8298?

1, 2, 3, 6, 9, 18, 461, 922, 1383, 2766, 4149, 8298

There is a total of 12 positive divisors.
The sum of these divisors is 18018.
The arithmetic mean is 1501.5.

6 even divisors

2, 6, 18, 922, 2766, 8298

6 odd divisors

1, 3, 9, 461, 1383, 4149

How to compute the divisors of 8298?

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 8298 by each of the numbers from 1 to 8298 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)

8298 / 1 = 8298 (the remainder is 0, so 1 is a divisor of 8298)
8298 / 2 = 4149 (the remainder is 0, so 2 is a divisor of 8298)
8298 / 3 = 2766 (the remainder is 0, so 3 is a divisor of 8298)
...
8298 / 8297 = 1.0001205254911 (the remainder is 1, so 8297 is not a divisor of 8298)
8298 / 8298 = 1 (the remainder is 0, so 8298 is a divisor of 8298)

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 8298 (i.e. 91.093358704134). 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 $\frac{N}{d} = D$ )

8298 / 1 = 8298 (the remainder is 0, so 1 and 8298 are divisors of 8298)
8298 / 2 = 4149 (the remainder is 0, so 2 and 4149 are divisors of 8298)
8298 / 3 = 2766 (the remainder is 0, so 3 and 2766 are divisors of 8298)
...
8298 / 90 = 92.2 (the remainder is 18, so 90 is not a divisor of 8298)
8298 / 91 = 91.186813186813 (the remainder is 17, so 91 is not a divisor of 8298)