What are the divisors of 9237?

1, 3, 3079, 9237

There is a total of 4 positive divisors.
The sum of these divisors is 12320.
The arithmetic mean is 3080.

4 odd divisors

1, 3, 3079, 9237

How to compute the divisors of 9237?

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 9237 by each of the numbers from 1 to 9237 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)

9237 / 1 = 9237 (the remainder is 0, so 1 is a divisor of 9237)
9237 / 2 = 4618.5 (the remainder is 1, so 2 is not a divisor of 9237)
9237 / 3 = 3079 (the remainder is 0, so 3 is a divisor of 9237)
...
9237 / 9236 = 1.0001082719792 (the remainder is 1, so 9236 is not a divisor of 9237)
9237 / 9237 = 1 (the remainder is 0, so 9237 is a divisor of 9237)

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 9237 (i.e. 96.109312764165). 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 $\frac{N}{d} = D$ )

9237 / 1 = 9237 (the remainder is 0, so 1 and 9237 are divisors of 9237)
9237 / 2 = 4618.5 (the remainder is 1, so 2 is not a divisor of 9237)
9237 / 3 = 3079 (the remainder is 0, so 3 and 3079 are divisors of 9237)
...
9237 / 95 = 97.231578947368 (the remainder is 22, so 95 is not a divisor of 9237)
9237 / 96 = 96.21875 (the remainder is 21, so 96 is not a divisor of 9237)