What are the divisors of 9224?

1, 2, 4, 8, 1153, 2306, 4612, 9224

There is a total of 8 positive divisors.
The sum of these divisors is 17310.
The arithmetic mean is 2163.75.

6 even divisors

2, 4, 8, 2306, 4612, 9224

2 odd divisors

1, 1153

How to compute the divisors of 9224?

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 9224 by each of the numbers from 1 to 9224 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)

9224 / 1 = 9224 (the remainder is 0, so 1 is a divisor of 9224)
9224 / 2 = 4612 (the remainder is 0, so 2 is a divisor of 9224)
9224 / 3 = 3074.6666666667 (the remainder is 2, so 3 is not a divisor of 9224)
...
9224 / 9223 = 1.0001084245907 (the remainder is 1, so 9223 is not a divisor of 9224)
9224 / 9224 = 1 (the remainder is 0, so 9224 is a divisor of 9224)

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 9224 (i.e. 96.041657628344). 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 $\frac{N}{d} = D$ )

9224 / 1 = 9224 (the remainder is 0, so 1 and 9224 are divisors of 9224)
9224 / 2 = 4612 (the remainder is 0, so 2 and 4612 are divisors of 9224)
9224 / 3 = 3074.6666666667 (the remainder is 2, so 3 is not a divisor of 9224)
...
9224 / 95 = 97.094736842105 (the remainder is 9, so 95 is not a divisor of 9224)
9224 / 96 = 96.083333333333 (the remainder is 8, so 96 is not a divisor of 9224)