What are the divisors of 9086?

1, 2, 7, 11, 14, 22, 59, 77, 118, 154, 413, 649, 826, 1298, 4543, 9086

There is a total of 16 positive divisors.
The sum of these divisors is 17280.
The arithmetic mean is 1080.

8 even divisors

2, 14, 22, 118, 154, 826, 1298, 9086

8 odd divisors

1, 7, 11, 59, 77, 413, 649, 4543

How to compute the divisors of 9086?

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 9086 by each of the numbers from 1 to 9086 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)

9086 / 1 = 9086 (the remainder is 0, so 1 is a divisor of 9086)
9086 / 2 = 4543 (the remainder is 0, so 2 is a divisor of 9086)
9086 / 3 = 3028.6666666667 (the remainder is 2, so 3 is not a divisor of 9086)
...
9086 / 9085 = 1.0001100715465 (the remainder is 1, so 9085 is not a divisor of 9086)
9086 / 9086 = 1 (the remainder is 0, so 9086 is a divisor of 9086)

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 9086 (i.e. 95.32051195834). 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 $\frac{N}{d} = D$ )

9086 / 1 = 9086 (the remainder is 0, so 1 and 9086 are divisors of 9086)
9086 / 2 = 4543 (the remainder is 0, so 2 and 4543 are divisors of 9086)
9086 / 3 = 3028.6666666667 (the remainder is 2, so 3 is not a divisor of 9086)
...
9086 / 94 = 96.659574468085 (the remainder is 62, so 94 is not a divisor of 9086)
9086 / 95 = 95.642105263158 (the remainder is 61, so 95 is not a divisor of 9086)