What are the divisors of 9226?

1, 2, 7, 14, 659, 1318, 4613, 9226

There is a total of 8 positive divisors.
The sum of these divisors is 15840.
The arithmetic mean is 1980.

4 even divisors

2, 14, 1318, 9226

4 odd divisors

1, 7, 659, 4613

How to compute the divisors of 9226?

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 9226 by each of the numbers from 1 to 9226 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)

9226 / 1 = 9226 (the remainder is 0, so 1 is a divisor of 9226)
9226 / 2 = 4613 (the remainder is 0, so 2 is a divisor of 9226)
9226 / 3 = 3075.3333333333 (the remainder is 1, so 3 is not a divisor of 9226)
...
9226 / 9225 = 1.000108401084 (the remainder is 1, so 9225 is not a divisor of 9226)
9226 / 9226 = 1 (the remainder is 0, so 9226 is a divisor of 9226)

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 9226 (i.e. 96.052069212485). 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 $\frac{N}{d} = D$ )

9226 / 1 = 9226 (the remainder is 0, so 1 and 9226 are divisors of 9226)
9226 / 2 = 4613 (the remainder is 0, so 2 and 4613 are divisors of 9226)
9226 / 3 = 3075.3333333333 (the remainder is 1, so 3 is not a divisor of 9226)
...
9226 / 95 = 97.115789473684 (the remainder is 11, so 95 is not a divisor of 9226)
9226 / 96 = 96.104166666667 (the remainder is 10, so 96 is not a divisor of 9226)