What are the divisors of 5711?

1, 5711

There is a total of 2 positive divisors.
The sum of these divisors is 5712.
The arithmetic mean is 2856.

2 odd divisors

1, 5711

How to compute the divisors of 5711?

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 5711 by each of the numbers from 1 to 5711 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)

5711 / 1 = 5711 (the remainder is 0, so 1 is a divisor of 5711)
5711 / 2 = 2855.5 (the remainder is 1, so 2 is not a divisor of 5711)
5711 / 3 = 1903.6666666667 (the remainder is 2, so 3 is not a divisor of 5711)
...
5711 / 5710 = 1.0001751313485 (the remainder is 1, so 5710 is not a divisor of 5711)
5711 / 5711 = 1 (the remainder is 0, so 5711 is a divisor of 5711)

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 5711 (i.e. 75.571158519636). 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 $\frac{N}{d} = D$ )

5711 / 1 = 5711 (the remainder is 0, so 1 and 5711 are divisors of 5711)
5711 / 2 = 2855.5 (the remainder is 1, so 2 is not a divisor of 5711)
5711 / 3 = 1903.6666666667 (the remainder is 2, so 3 is not a divisor of 5711)
...
5711 / 74 = 77.175675675676 (the remainder is 13, so 74 is not a divisor of 5711)
5711 / 75 = 76.146666666667 (the remainder is 11, so 75 is not a divisor of 5711)