What are the divisors of 9236?

1, 2, 4, 2309, 4618, 9236

There is a total of 6 positive divisors.
The sum of these divisors is 16170.
The arithmetic mean is 2695.

4 even divisors

2, 4, 4618, 9236

2 odd divisors

1, 2309

How to compute the divisors of 9236?

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 9236 by each of the numbers from 1 to 9236 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)

9236 / 1 = 9236 (the remainder is 0, so 1 is a divisor of 9236)
9236 / 2 = 4618 (the remainder is 0, so 2 is a divisor of 9236)
9236 / 3 = 3078.6666666667 (the remainder is 2, so 3 is not a divisor of 9236)
...
9236 / 9235 = 1.0001082837033 (the remainder is 1, so 9235 is not a divisor of 9236)
9236 / 9236 = 1 (the remainder is 0, so 9236 is a divisor of 9236)

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 9236 (i.e. 96.104110213872). 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 $\frac{N}{d} = D$ )

9236 / 1 = 9236 (the remainder is 0, so 1 and 9236 are divisors of 9236)
9236 / 2 = 4618 (the remainder is 0, so 2 and 4618 are divisors of 9236)
9236 / 3 = 3078.6666666667 (the remainder is 2, so 3 is not a divisor of 9236)
...
9236 / 95 = 97.221052631579 (the remainder is 21, so 95 is not a divisor of 9236)
9236 / 96 = 96.208333333333 (the remainder is 20, so 96 is not a divisor of 9236)