What are the divisors of 5686?

1, 2, 2843, 5686

There is a total of 4 positive divisors.
The sum of these divisors is 8532.
The arithmetic mean is 2133.

2 even divisors

2, 5686

2 odd divisors

1, 2843

How to compute the divisors of 5686?

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 5686 by each of the numbers from 1 to 5686 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)

5686 / 1 = 5686 (the remainder is 0, so 1 is a divisor of 5686)
5686 / 2 = 2843 (the remainder is 0, so 2 is a divisor of 5686)
5686 / 3 = 1895.3333333333 (the remainder is 1, so 3 is not a divisor of 5686)
...
5686 / 5685 = 1.0001759014952 (the remainder is 1, so 5685 is not a divisor of 5686)
5686 / 5686 = 1 (the remainder is 0, so 5686 is a divisor of 5686)

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 5686 (i.e. 75.405570086035). 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 $\frac{N}{d} = D$ )

5686 / 1 = 5686 (the remainder is 0, so 1 and 5686 are divisors of 5686)
5686 / 2 = 2843 (the remainder is 0, so 2 and 2843 are divisors of 5686)
5686 / 3 = 1895.3333333333 (the remainder is 1, so 3 is not a divisor of 5686)
...
5686 / 74 = 76.837837837838 (the remainder is 62, so 74 is not a divisor of 5686)
5686 / 75 = 75.813333333333 (the remainder is 61, so 75 is not a divisor of 5686)