What are the divisors of 9213?

1, 3, 37, 83, 111, 249, 3071, 9213

There is a total of 8 positive divisors.
The sum of these divisors is 12768.
The arithmetic mean is 1596.

8 odd divisors

1, 3, 37, 83, 111, 249, 3071, 9213

How to compute the divisors of 9213?

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 9213 by each of the numbers from 1 to 9213 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)

9213 / 1 = 9213 (the remainder is 0, so 1 is a divisor of 9213)
9213 / 2 = 4606.5 (the remainder is 1, so 2 is not a divisor of 9213)
9213 / 3 = 3071 (the remainder is 0, so 3 is a divisor of 9213)
...
9213 / 9212 = 1.0001085540599 (the remainder is 1, so 9212 is not a divisor of 9213)
9213 / 9213 = 1 (the remainder is 0, so 9213 is a divisor of 9213)

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 9213 (i.e. 95.984373728227). 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 $\frac{N}{d} = D$ )

9213 / 1 = 9213 (the remainder is 0, so 1 and 9213 are divisors of 9213)
9213 / 2 = 4606.5 (the remainder is 1, so 2 is not a divisor of 9213)
9213 / 3 = 3071 (the remainder is 0, so 3 and 3071 are divisors of 9213)
...
9213 / 94 = 98.010638297872 (the remainder is 1, so 94 is not a divisor of 9213)
9213 / 95 = 96.978947368421 (the remainder is 93, so 95 is not a divisor of 9213)