What are the divisors of 7089?

1, 3, 17, 51, 139, 417, 2363, 7089

There is a total of 8 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 1260.

8 odd divisors

1, 3, 17, 51, 139, 417, 2363, 7089

How to compute the divisors of 7089?

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 7089 by each of the numbers from 1 to 7089 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)

7089 / 1 = 7089 (the remainder is 0, so 1 is a divisor of 7089)
7089 / 2 = 3544.5 (the remainder is 1, so 2 is not a divisor of 7089)
7089 / 3 = 2363 (the remainder is 0, so 3 is a divisor of 7089)
...
7089 / 7088 = 1.0001410835214 (the remainder is 1, so 7088 is not a divisor of 7089)
7089 / 7089 = 1 (the remainder is 0, so 7089 is a divisor of 7089)

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 7089 (i.e. 84.196199439167). 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 $\frac{N}{d} = D$ )

7089 / 1 = 7089 (the remainder is 0, so 1 and 7089 are divisors of 7089)
7089 / 2 = 3544.5 (the remainder is 1, so 2 is not a divisor of 7089)
7089 / 3 = 2363 (the remainder is 0, so 3 and 2363 are divisors of 7089)
...
7089 / 83 = 85.409638554217 (the remainder is 34, so 83 is not a divisor of 7089)
7089 / 84 = 84.392857142857 (the remainder is 33, so 84 is not a divisor of 7089)