What are the divisors of 5718?

1, 2, 3, 6, 953, 1906, 2859, 5718

There is a total of 8 positive divisors.
The sum of these divisors is 11448.
The arithmetic mean is 1431.

4 even divisors

2, 6, 1906, 5718

4 odd divisors

1, 3, 953, 2859

How to compute the divisors of 5718?

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 5718 by each of the numbers from 1 to 5718 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)

5718 / 1 = 5718 (the remainder is 0, so 1 is a divisor of 5718)
5718 / 2 = 2859 (the remainder is 0, so 2 is a divisor of 5718)
5718 / 3 = 1906 (the remainder is 0, so 3 is a divisor of 5718)
...
5718 / 5717 = 1.0001749169145 (the remainder is 1, so 5717 is not a divisor of 5718)
5718 / 5718 = 1 (the remainder is 0, so 5718 is a divisor of 5718)

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 5718 (i.e. 75.617458301638). 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 $\frac{N}{d} = D$ )

5718 / 1 = 5718 (the remainder is 0, so 1 and 5718 are divisors of 5718)
5718 / 2 = 2859 (the remainder is 0, so 2 and 2859 are divisors of 5718)
5718 / 3 = 1906 (the remainder is 0, so 3 and 1906 are divisors of 5718)
...
5718 / 74 = 77.27027027027 (the remainder is 20, so 74 is not a divisor of 5718)
5718 / 75 = 76.24 (the remainder is 18, so 75 is not a divisor of 5718)