What are the divisors of 9128?

1, 2, 4, 7, 8, 14, 28, 56, 163, 326, 652, 1141, 1304, 2282, 4564, 9128

There is a total of 16 positive divisors.
The sum of these divisors is 19680.
The arithmetic mean is 1230.

12 even divisors

2, 4, 8, 14, 28, 56, 326, 652, 1304, 2282, 4564, 9128

4 odd divisors

1, 7, 163, 1141

How to compute the divisors of 9128?

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 9128 by each of the numbers from 1 to 9128 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)

9128 / 1 = 9128 (the remainder is 0, so 1 is a divisor of 9128)
9128 / 2 = 4564 (the remainder is 0, so 2 is a divisor of 9128)
9128 / 3 = 3042.6666666667 (the remainder is 2, so 3 is not a divisor of 9128)
...
9128 / 9127 = 1.0001095650268 (the remainder is 1, so 9127 is not a divisor of 9128)
9128 / 9128 = 1 (the remainder is 0, so 9128 is a divisor of 9128)

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 9128 (i.e. 95.540567299969). 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 $\frac{N}{d} = D$ )

9128 / 1 = 9128 (the remainder is 0, so 1 and 9128 are divisors of 9128)
9128 / 2 = 4564 (the remainder is 0, so 2 and 4564 are divisors of 9128)
9128 / 3 = 3042.6666666667 (the remainder is 2, so 3 is not a divisor of 9128)
...
9128 / 94 = 97.106382978723 (the remainder is 10, so 94 is not a divisor of 9128)
9128 / 95 = 96.084210526316 (the remainder is 8, so 95 is not a divisor of 9128)