What are the divisors of 9096?

1, 2, 3, 4, 6, 8, 12, 24, 379, 758, 1137, 1516, 2274, 3032, 4548, 9096

There is a total of 16 positive divisors.
The sum of these divisors is 22800.
The arithmetic mean is 1425.

12 even divisors

2, 4, 6, 8, 12, 24, 758, 1516, 2274, 3032, 4548, 9096

4 odd divisors

1, 3, 379, 1137

How to compute the divisors of 9096?

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 9096 by each of the numbers from 1 to 9096 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)

9096 / 1 = 9096 (the remainder is 0, so 1 is a divisor of 9096)
9096 / 2 = 4548 (the remainder is 0, so 2 is a divisor of 9096)
9096 / 3 = 3032 (the remainder is 0, so 3 is a divisor of 9096)
...
9096 / 9095 = 1.0001099505223 (the remainder is 1, so 9095 is not a divisor of 9096)
9096 / 9096 = 1 (the remainder is 0, so 9096 is a divisor of 9096)

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 9096 (i.e. 95.372952140531). 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 $\frac{N}{d} = D$ )

9096 / 1 = 9096 (the remainder is 0, so 1 and 9096 are divisors of 9096)
9096 / 2 = 4548 (the remainder is 0, so 2 and 4548 are divisors of 9096)
9096 / 3 = 3032 (the remainder is 0, so 3 and 3032 are divisors of 9096)
...
9096 / 94 = 96.765957446809 (the remainder is 72, so 94 is not a divisor of 9096)
9096 / 95 = 95.747368421053 (the remainder is 71, so 95 is not a divisor of 9096)