What are the divisors of 9233?

1, 7, 1319, 9233

There is a total of 4 positive divisors.
The sum of these divisors is 10560.
The arithmetic mean is 2640.

4 odd divisors

1, 7, 1319, 9233

How to compute the divisors of 9233?

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 9233 by each of the numbers from 1 to 9233 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)

9233 / 1 = 9233 (the remainder is 0, so 1 is a divisor of 9233)
9233 / 2 = 4616.5 (the remainder is 1, so 2 is not a divisor of 9233)
9233 / 3 = 3077.6666666667 (the remainder is 2, so 3 is not a divisor of 9233)
...
9233 / 9232 = 1.0001083188908 (the remainder is 1, so 9232 is not a divisor of 9233)
9233 / 9233 = 1 (the remainder is 0, so 9233 is a divisor of 9233)

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 9233 (i.e. 96.088500872893). 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 $\frac{N}{d} = D$ )

9233 / 1 = 9233 (the remainder is 0, so 1 and 9233 are divisors of 9233)
9233 / 2 = 4616.5 (the remainder is 1, so 2 is not a divisor of 9233)
9233 / 3 = 3077.6666666667 (the remainder is 2, so 3 is not a divisor of 9233)
...
9233 / 95 = 97.189473684211 (the remainder is 18, so 95 is not a divisor of 9233)
9233 / 96 = 96.177083333333 (the remainder is 17, so 96 is not a divisor of 9233)