What are the divisors of 5726?

1, 2, 7, 14, 409, 818, 2863, 5726

There is a total of 8 positive divisors.
The sum of these divisors is 9840.
The arithmetic mean is 1230.

4 even divisors

2, 14, 818, 5726

4 odd divisors

1, 7, 409, 2863

How to compute the divisors of 5726?

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 5726 by each of the numbers from 1 to 5726 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)

5726 / 1 = 5726 (the remainder is 0, so 1 is a divisor of 5726)
5726 / 2 = 2863 (the remainder is 0, so 2 is a divisor of 5726)
5726 / 3 = 1908.6666666667 (the remainder is 2, so 3 is not a divisor of 5726)
...
5726 / 5725 = 1.0001746724891 (the remainder is 1, so 5725 is not a divisor of 5726)
5726 / 5726 = 1 (the remainder is 0, so 5726 is a divisor of 5726)

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 5726 (i.e. 75.67033764957). 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 $\frac{N}{d} = D$ )

5726 / 1 = 5726 (the remainder is 0, so 1 and 5726 are divisors of 5726)
5726 / 2 = 2863 (the remainder is 0, so 2 and 2863 are divisors of 5726)
5726 / 3 = 1908.6666666667 (the remainder is 2, so 3 is not a divisor of 5726)
...
5726 / 74 = 77.378378378378 (the remainder is 28, so 74 is not a divisor of 5726)
5726 / 75 = 76.346666666667 (the remainder is 26, so 75 is not a divisor of 5726)