What are the divisors of 9187?

1, 9187

There is a total of 2 positive divisors.
The sum of these divisors is 9188.
The arithmetic mean is 4594.

2 odd divisors

1, 9187

How to compute the divisors of 9187?

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 9187 by each of the numbers from 1 to 9187 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)

9187 / 1 = 9187 (the remainder is 0, so 1 is a divisor of 9187)
9187 / 2 = 4593.5 (the remainder is 1, so 2 is not a divisor of 9187)
9187 / 3 = 3062.3333333333 (the remainder is 1, so 3 is not a divisor of 9187)
...
9187 / 9186 = 1.0001088613107 (the remainder is 1, so 9186 is not a divisor of 9187)
9187 / 9187 = 1 (the remainder is 0, so 9187 is a divisor of 9187)

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 9187 (i.e. 95.848839325263). 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 $\frac{N}{d} = D$ )

9187 / 1 = 9187 (the remainder is 0, so 1 and 9187 are divisors of 9187)
9187 / 2 = 4593.5 (the remainder is 1, so 2 is not a divisor of 9187)
9187 / 3 = 3062.3333333333 (the remainder is 1, so 3 is not a divisor of 9187)
...
9187 / 94 = 97.734042553191 (the remainder is 69, so 94 is not a divisor of 9187)
9187 / 95 = 96.705263157895 (the remainder is 67, so 95 is not a divisor of 9187)