What are the divisors of 9166?

1, 2, 4583, 9166

There is a total of 4 positive divisors.
The sum of these divisors is 13752.
The arithmetic mean is 3438.

2 even divisors

2, 9166

2 odd divisors

1, 4583

How to compute the divisors of 9166?

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 9166 by each of the numbers from 1 to 9166 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)

9166 / 1 = 9166 (the remainder is 0, so 1 is a divisor of 9166)
9166 / 2 = 4583 (the remainder is 0, so 2 is a divisor of 9166)
9166 / 3 = 3055.3333333333 (the remainder is 1, so 3 is not a divisor of 9166)
...
9166 / 9165 = 1.0001091107474 (the remainder is 1, so 9165 is not a divisor of 9166)
9166 / 9166 = 1 (the remainder is 0, so 9166 is a divisor of 9166)

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 9166 (i.e. 95.739229159211). 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 $\frac{N}{d} = D$ )

9166 / 1 = 9166 (the remainder is 0, so 1 and 9166 are divisors of 9166)
9166 / 2 = 4583 (the remainder is 0, so 2 and 4583 are divisors of 9166)
9166 / 3 = 3055.3333333333 (the remainder is 1, so 3 is not a divisor of 9166)
...
9166 / 94 = 97.510638297872 (the remainder is 48, so 94 is not a divisor of 9166)
9166 / 95 = 96.484210526316 (the remainder is 46, so 95 is not a divisor of 9166)