What are the divisors of 5706?

1, 2, 3, 6, 9, 18, 317, 634, 951, 1902, 2853, 5706

There is a total of 12 positive divisors.
The sum of these divisors is 12402.
The arithmetic mean is 1033.5.

6 even divisors

2, 6, 18, 634, 1902, 5706

6 odd divisors

1, 3, 9, 317, 951, 2853

How to compute the divisors of 5706?

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 5706 by each of the numbers from 1 to 5706 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)

5706 / 1 = 5706 (the remainder is 0, so 1 is a divisor of 5706)
5706 / 2 = 2853 (the remainder is 0, so 2 is a divisor of 5706)
5706 / 3 = 1902 (the remainder is 0, so 3 is a divisor of 5706)
...
5706 / 5705 = 1.0001752848379 (the remainder is 1, so 5705 is not a divisor of 5706)
5706 / 5706 = 1 (the remainder is 0, so 5706 is a divisor of 5706)

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 5706 (i.e. 75.538069872085). 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 $\frac{N}{d} = D$ )

5706 / 1 = 5706 (the remainder is 0, so 1 and 5706 are divisors of 5706)
5706 / 2 = 2853 (the remainder is 0, so 2 and 2853 are divisors of 5706)
5706 / 3 = 1902 (the remainder is 0, so 3 and 1902 are divisors of 5706)
...
5706 / 74 = 77.108108108108 (the remainder is 8, so 74 is not a divisor of 5706)
5706 / 75 = 76.08 (the remainder is 6, so 75 is not a divisor of 5706)