What are the divisors of 8186?

1, 2, 4093, 8186

There is a total of 4 positive divisors.
The sum of these divisors is 12282.
The arithmetic mean is 3070.5.

2 even divisors

2, 8186

2 odd divisors

1, 4093

How to compute the divisors of 8186?

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 8186 by each of the numbers from 1 to 8186 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)

8186 / 1 = 8186 (the remainder is 0, so 1 is a divisor of 8186)
8186 / 2 = 4093 (the remainder is 0, so 2 is a divisor of 8186)
8186 / 3 = 2728.6666666667 (the remainder is 2, so 3 is not a divisor of 8186)
...
8186 / 8185 = 1.0001221747098 (the remainder is 1, so 8185 is not a divisor of 8186)
8186 / 8186 = 1 (the remainder is 0, so 8186 is a divisor of 8186)

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 8186 (i.e. 90.47651629014). 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 $\frac{N}{d} = D$ )

8186 / 1 = 8186 (the remainder is 0, so 1 and 8186 are divisors of 8186)
8186 / 2 = 4093 (the remainder is 0, so 2 and 4093 are divisors of 8186)
8186 / 3 = 2728.6666666667 (the remainder is 2, so 3 is not a divisor of 8186)
...
8186 / 89 = 91.977528089888 (the remainder is 87, so 89 is not a divisor of 8186)
8186 / 90 = 90.955555555556 (the remainder is 86, so 90 is not a divisor of 8186)