What are the divisors of 9239?

1, 9239

There is a total of 2 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 4620.

2 odd divisors

1, 9239

How to compute the divisors of 9239?

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 9239 by each of the numbers from 1 to 9239 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)

9239 / 1 = 9239 (the remainder is 0, so 1 is a divisor of 9239)
9239 / 2 = 4619.5 (the remainder is 1, so 2 is not a divisor of 9239)
9239 / 3 = 3079.6666666667 (the remainder is 2, so 3 is not a divisor of 9239)
...
9239 / 9238 = 1.0001082485386 (the remainder is 1, so 9238 is not a divisor of 9239)
9239 / 9239 = 1 (the remainder is 0, so 9239 is a divisor of 9239)

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 9239 (i.e. 96.119717019975). 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 $\frac{N}{d} = D$ )

9239 / 1 = 9239 (the remainder is 0, so 1 and 9239 are divisors of 9239)
9239 / 2 = 4619.5 (the remainder is 1, so 2 is not a divisor of 9239)
9239 / 3 = 3079.6666666667 (the remainder is 2, so 3 is not a divisor of 9239)
...
9239 / 95 = 97.252631578947 (the remainder is 24, so 95 is not a divisor of 9239)
9239 / 96 = 96.239583333333 (the remainder is 23, so 96 is not a divisor of 9239)