What are the divisors of 9039?

1, 3, 23, 69, 131, 393, 3013, 9039

There is a total of 8 positive divisors.
The sum of these divisors is 12672.
The arithmetic mean is 1584.

8 odd divisors

1, 3, 23, 69, 131, 393, 3013, 9039

How to compute the divisors of 9039?

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 9039 by each of the numbers from 1 to 9039 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)

9039 / 1 = 9039 (the remainder is 0, so 1 is a divisor of 9039)
9039 / 2 = 4519.5 (the remainder is 1, so 2 is not a divisor of 9039)
9039 / 3 = 3013 (the remainder is 0, so 3 is a divisor of 9039)
...
9039 / 9038 = 1.0001106439478 (the remainder is 1, so 9038 is not a divisor of 9039)
9039 / 9039 = 1 (the remainder is 0, so 9039 is a divisor of 9039)

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 9039 (i.e. 95.073655657075). 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 $\frac{N}{d} = D$ )

9039 / 1 = 9039 (the remainder is 0, so 1 and 9039 are divisors of 9039)
9039 / 2 = 4519.5 (the remainder is 1, so 2 is not a divisor of 9039)
9039 / 3 = 3013 (the remainder is 0, so 3 and 3013 are divisors of 9039)
...
9039 / 94 = 96.159574468085 (the remainder is 15, so 94 is not a divisor of 9039)
9039 / 95 = 95.147368421053 (the remainder is 14, so 95 is not a divisor of 9039)