What are the divisors of 9123?

1, 3, 3041, 9123

There is a total of 4 positive divisors.
The sum of these divisors is 12168.
The arithmetic mean is 3042.

4 odd divisors

1, 3, 3041, 9123

How to compute the divisors of 9123?

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 9123 by each of the numbers from 1 to 9123 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)

9123 / 1 = 9123 (the remainder is 0, so 1 is a divisor of 9123)
9123 / 2 = 4561.5 (the remainder is 1, so 2 is not a divisor of 9123)
9123 / 3 = 3041 (the remainder is 0, so 3 is a divisor of 9123)
...
9123 / 9122 = 1.0001096250822 (the remainder is 1, so 9122 is not a divisor of 9123)
9123 / 9123 = 1 (the remainder is 0, so 9123 is a divisor of 9123)

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 9123 (i.e. 95.514396820584). 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 $\frac{N}{d} = D$ )

9123 / 1 = 9123 (the remainder is 0, so 1 and 9123 are divisors of 9123)
9123 / 2 = 4561.5 (the remainder is 1, so 2 is not a divisor of 9123)
9123 / 3 = 3041 (the remainder is 0, so 3 and 3041 are divisors of 9123)
...
9123 / 94 = 97.053191489362 (the remainder is 5, so 94 is not a divisor of 9123)
9123 / 95 = 96.031578947368 (the remainder is 3, so 95 is not a divisor of 9123)