What are the divisors of 9186?

1, 2, 3, 6, 1531, 3062, 4593, 9186

There is a total of 8 positive divisors.
The sum of these divisors is 18384.
The arithmetic mean is 2298.

4 even divisors

2, 6, 3062, 9186

4 odd divisors

1, 3, 1531, 4593

How to compute the divisors of 9186?

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 9186 by each of the numbers from 1 to 9186 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)

9186 / 1 = 9186 (the remainder is 0, so 1 is a divisor of 9186)
9186 / 2 = 4593 (the remainder is 0, so 2 is a divisor of 9186)
9186 / 3 = 3062 (the remainder is 0, so 3 is a divisor of 9186)
...
9186 / 9185 = 1.0001088731628 (the remainder is 1, so 9185 is not a divisor of 9186)
9186 / 9186 = 1 (the remainder is 0, so 9186 is a divisor of 9186)

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 9186 (i.e. 95.843622636042). 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 $\frac{N}{d} = D$ )

9186 / 1 = 9186 (the remainder is 0, so 1 and 9186 are divisors of 9186)
9186 / 2 = 4593 (the remainder is 0, so 2 and 4593 are divisors of 9186)
9186 / 3 = 3062 (the remainder is 0, so 3 and 3062 are divisors of 9186)
...
9186 / 94 = 97.723404255319 (the remainder is 68, so 94 is not a divisor of 9186)
9186 / 95 = 96.694736842105 (the remainder is 66, so 95 is not a divisor of 9186)