What are the divisors of 9188?

1, 2, 4, 2297, 4594, 9188

There is a total of 6 positive divisors.
The sum of these divisors is 16086.
The arithmetic mean is 2681.

4 even divisors

2, 4, 4594, 9188

2 odd divisors

1, 2297

How to compute the divisors of 9188?

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 9188 by each of the numbers from 1 to 9188 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)

9188 / 1 = 9188 (the remainder is 0, so 1 is a divisor of 9188)
9188 / 2 = 4594 (the remainder is 0, so 2 is a divisor of 9188)
9188 / 3 = 3062.6666666667 (the remainder is 2, so 3 is not a divisor of 9188)
...
9188 / 9187 = 1.0001088494612 (the remainder is 1, so 9187 is not a divisor of 9188)
9188 / 9188 = 1 (the remainder is 0, so 9188 is a divisor of 9188)

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 9188 (i.e. 95.854055730574). 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 $\frac{N}{d} = D$ )

9188 / 1 = 9188 (the remainder is 0, so 1 and 9188 are divisors of 9188)
9188 / 2 = 4594 (the remainder is 0, so 2 and 4594 are divisors of 9188)
9188 / 3 = 3062.6666666667 (the remainder is 2, so 3 is not a divisor of 9188)
...
9188 / 94 = 97.744680851064 (the remainder is 70, so 94 is not a divisor of 9188)
9188 / 95 = 96.715789473684 (the remainder is 68, so 95 is not a divisor of 9188)