What are the divisors of 7086?

1, 2, 3, 6, 1181, 2362, 3543, 7086

There is a total of 8 positive divisors.
The sum of these divisors is 14184.
The arithmetic mean is 1773.

4 even divisors

2, 6, 2362, 7086

4 odd divisors

1, 3, 1181, 3543

How to compute the divisors of 7086?

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 7086 by each of the numbers from 1 to 7086 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)

7086 / 1 = 7086 (the remainder is 0, so 1 is a divisor of 7086)
7086 / 2 = 3543 (the remainder is 0, so 2 is a divisor of 7086)
7086 / 3 = 2362 (the remainder is 0, so 3 is a divisor of 7086)
...
7086 / 7085 = 1.0001411432604 (the remainder is 1, so 7085 is not a divisor of 7086)
7086 / 7086 = 1 (the remainder is 0, so 7086 is a divisor of 7086)

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 7086 (i.e. 84.17838202294). 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 $\frac{N}{d} = D$ )

7086 / 1 = 7086 (the remainder is 0, so 1 and 7086 are divisors of 7086)
7086 / 2 = 3543 (the remainder is 0, so 2 and 3543 are divisors of 7086)
7086 / 3 = 2362 (the remainder is 0, so 3 and 2362 are divisors of 7086)
...
7086 / 83 = 85.373493975904 (the remainder is 31, so 83 is not a divisor of 7086)
7086 / 84 = 84.357142857143 (the remainder is 30, so 84 is not a divisor of 7086)