What are the divisors of 5807?

1, 5807

There is a total of 2 positive divisors.
The sum of these divisors is 5808.
The arithmetic mean is 2904.

2 odd divisors

1, 5807

How to compute the divisors of 5807?

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 5807 by each of the numbers from 1 to 5807 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)

5807 / 1 = 5807 (the remainder is 0, so 1 is a divisor of 5807)
5807 / 2 = 2903.5 (the remainder is 1, so 2 is not a divisor of 5807)
5807 / 3 = 1935.6666666667 (the remainder is 2, so 3 is not a divisor of 5807)
...
5807 / 5806 = 1.0001722356183 (the remainder is 1, so 5806 is not a divisor of 5807)
5807 / 5807 = 1 (the remainder is 0, so 5807 is a divisor of 5807)

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 5807 (i.e. 76.203674452089). 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 $\frac{N}{d} = D$ )

5807 / 1 = 5807 (the remainder is 0, so 1 and 5807 are divisors of 5807)
5807 / 2 = 2903.5 (the remainder is 1, so 2 is not a divisor of 5807)
5807 / 3 = 1935.6666666667 (the remainder is 2, so 3 is not a divisor of 5807)
...
5807 / 75 = 77.426666666667 (the remainder is 32, so 75 is not a divisor of 5807)
5807 / 76 = 76.407894736842 (the remainder is 31, so 76 is not a divisor of 5807)