What are the divisors of 5717?

1, 5717

There is a total of 2 positive divisors.
The sum of these divisors is 5718.
The arithmetic mean is 2859.

2 odd divisors

1, 5717

How to compute the divisors of 5717?

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 5717 by each of the numbers from 1 to 5717 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)

5717 / 1 = 5717 (the remainder is 0, so 1 is a divisor of 5717)
5717 / 2 = 2858.5 (the remainder is 1, so 2 is not a divisor of 5717)
5717 / 3 = 1905.6666666667 (the remainder is 2, so 3 is not a divisor of 5717)
...
5717 / 5716 = 1.0001749475157 (the remainder is 1, so 5716 is not a divisor of 5717)
5717 / 5717 = 1 (the remainder is 0, so 5717 is a divisor of 5717)

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 5717 (i.e. 75.610845782864). 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 $\frac{N}{d} = D$ )

5717 / 1 = 5717 (the remainder is 0, so 1 and 5717 are divisors of 5717)
5717 / 2 = 2858.5 (the remainder is 1, so 2 is not a divisor of 5717)
5717 / 3 = 1905.6666666667 (the remainder is 2, so 3 is not a divisor of 5717)
...
5717 / 74 = 77.256756756757 (the remainder is 19, so 74 is not a divisor of 5717)
5717 / 75 = 76.226666666667 (the remainder is 17, so 75 is not a divisor of 5717)