What are the divisors of 5727?

1, 3, 23, 69, 83, 249, 1909, 5727

There is a total of 8 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1008.

8 odd divisors

1, 3, 23, 69, 83, 249, 1909, 5727

How to compute the divisors of 5727?

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 5727 by each of the numbers from 1 to 5727 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)

5727 / 1 = 5727 (the remainder is 0, so 1 is a divisor of 5727)
5727 / 2 = 2863.5 (the remainder is 1, so 2 is not a divisor of 5727)
5727 / 3 = 1909 (the remainder is 0, so 3 is a divisor of 5727)
...
5727 / 5726 = 1.0001746419839 (the remainder is 1, so 5726 is not a divisor of 5727)
5727 / 5727 = 1 (the remainder is 0, so 5727 is a divisor of 5727)

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 5727 (i.e. 75.67694497005). 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 $\frac{N}{d} = D$ )

5727 / 1 = 5727 (the remainder is 0, so 1 and 5727 are divisors of 5727)
5727 / 2 = 2863.5 (the remainder is 1, so 2 is not a divisor of 5727)
5727 / 3 = 1909 (the remainder is 0, so 3 and 1909 are divisors of 5727)
...
5727 / 74 = 77.391891891892 (the remainder is 29, so 74 is not a divisor of 5727)
5727 / 75 = 76.36 (the remainder is 27, so 75 is not a divisor of 5727)