What are the divisors of 8286?

1, 2, 3, 6, 1381, 2762, 4143, 8286

There is a total of 8 positive divisors.
The sum of these divisors is 16584.
The arithmetic mean is 2073.

4 even divisors

2, 6, 2762, 8286

4 odd divisors

1, 3, 1381, 4143

How to compute the divisors of 8286?

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 8286 by each of the numbers from 1 to 8286 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)

8286 / 1 = 8286 (the remainder is 0, so 1 is a divisor of 8286)
8286 / 2 = 4143 (the remainder is 0, so 2 is a divisor of 8286)
8286 / 3 = 2762 (the remainder is 0, so 3 is a divisor of 8286)
...
8286 / 8285 = 1.0001207000604 (the remainder is 1, so 8285 is not a divisor of 8286)
8286 / 8286 = 1 (the remainder is 0, so 8286 is a divisor of 8286)

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 8286 (i.e. 91.027468381802). 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 $\frac{N}{d} = D$ )

8286 / 1 = 8286 (the remainder is 0, so 1 and 8286 are divisors of 8286)
8286 / 2 = 4143 (the remainder is 0, so 2 and 4143 are divisors of 8286)
8286 / 3 = 2762 (the remainder is 0, so 3 and 2762 are divisors of 8286)
...
8286 / 90 = 92.066666666667 (the remainder is 6, so 90 is not a divisor of 8286)
8286 / 91 = 91.054945054945 (the remainder is 5, so 91 is not a divisor of 8286)