What are the divisors of 9189?

1, 3, 9, 1021, 3063, 9189

There is a total of 6 positive divisors.
The sum of these divisors is 13286.
The arithmetic mean is 2214.3333333333.

6 odd divisors

1, 3, 9, 1021, 3063, 9189

How to compute the divisors of 9189?

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 9189 by each of the numbers from 1 to 9189 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)

9189 / 1 = 9189 (the remainder is 0, so 1 is a divisor of 9189)
9189 / 2 = 4594.5 (the remainder is 1, so 2 is not a divisor of 9189)
9189 / 3 = 3063 (the remainder is 0, so 3 is a divisor of 9189)
...
9189 / 9188 = 1.0001088376143 (the remainder is 1, so 9188 is not a divisor of 9189)
9189 / 9189 = 1 (the remainder is 0, so 9189 is a divisor of 9189)

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 9189 (i.e. 95.859271852023). 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 $\frac{N}{d} = D$ )

9189 / 1 = 9189 (the remainder is 0, so 1 and 9189 are divisors of 9189)
9189 / 2 = 4594.5 (the remainder is 1, so 2 is not a divisor of 9189)
9189 / 3 = 3063 (the remainder is 0, so 3 and 3063 are divisors of 9189)
...
9189 / 94 = 97.755319148936 (the remainder is 71, so 94 is not a divisor of 9189)
9189 / 95 = 96.726315789474 (the remainder is 69, so 95 is not a divisor of 9189)