What are the divisors of 5710?

1, 2, 5, 10, 571, 1142, 2855, 5710

There is a total of 8 positive divisors.
The sum of these divisors is 10296.
The arithmetic mean is 1287.

4 even divisors

2, 10, 1142, 5710

4 odd divisors

1, 5, 571, 2855

How to compute the divisors of 5710?

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 5710 by each of the numbers from 1 to 5710 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)

5710 / 1 = 5710 (the remainder is 0, so 1 is a divisor of 5710)
5710 / 2 = 2855 (the remainder is 0, so 2 is a divisor of 5710)
5710 / 3 = 1903.3333333333 (the remainder is 1, so 3 is not a divisor of 5710)
...
5710 / 5709 = 1.0001751620249 (the remainder is 1, so 5709 is not a divisor of 5710)
5710 / 5710 = 1 (the remainder is 0, so 5710 is a divisor of 5710)

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 5710 (i.e. 75.56454194925). 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 $\frac{N}{d} = D$ )

5710 / 1 = 5710 (the remainder is 0, so 1 and 5710 are divisors of 5710)
5710 / 2 = 2855 (the remainder is 0, so 2 and 2855 are divisors of 5710)
5710 / 3 = 1903.3333333333 (the remainder is 1, so 3 is not a divisor of 5710)
...
5710 / 74 = 77.162162162162 (the remainder is 12, so 74 is not a divisor of 5710)
5710 / 75 = 76.133333333333 (the remainder is 10, so 75 is not a divisor of 5710)