What are the divisors of 9228?

1, 2, 3, 4, 6, 12, 769, 1538, 2307, 3076, 4614, 9228

There is a total of 12 positive divisors.
The sum of these divisors is 21560.
The arithmetic mean is 1796.6666666667.

8 even divisors

2, 4, 6, 12, 1538, 3076, 4614, 9228

4 odd divisors

1, 3, 769, 2307

How to compute the divisors of 9228?

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 9228 by each of the numbers from 1 to 9228 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)

9228 / 1 = 9228 (the remainder is 0, so 1 is a divisor of 9228)
9228 / 2 = 4614 (the remainder is 0, so 2 is a divisor of 9228)
9228 / 3 = 3076 (the remainder is 0, so 3 is a divisor of 9228)
...
9228 / 9227 = 1.0001083775875 (the remainder is 1, so 9227 is not a divisor of 9228)
9228 / 9228 = 1 (the remainder is 0, so 9228 is a divisor of 9228)

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 9228 (i.e. 96.062479668183). 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 $\frac{N}{d} = D$ )

9228 / 1 = 9228 (the remainder is 0, so 1 and 9228 are divisors of 9228)
9228 / 2 = 4614 (the remainder is 0, so 2 and 4614 are divisors of 9228)
9228 / 3 = 3076 (the remainder is 0, so 3 and 3076 are divisors of 9228)
...
9228 / 95 = 97.136842105263 (the remainder is 13, so 95 is not a divisor of 9228)
9228 / 96 = 96.125 (the remainder is 12, so 96 is not a divisor of 9228)