What are the divisors of 5766?

1, 2, 3, 6, 31, 62, 93, 186, 961, 1922, 2883, 5766

There is a total of 12 positive divisors.
The sum of these divisors is 11916.
The arithmetic mean is 993.

6 even divisors

2, 6, 62, 186, 1922, 5766

6 odd divisors

1, 3, 31, 93, 961, 2883

How to compute the divisors of 5766?

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 5766 by each of the numbers from 1 to 5766 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)

5766 / 1 = 5766 (the remainder is 0, so 1 is a divisor of 5766)
5766 / 2 = 2883 (the remainder is 0, so 2 is a divisor of 5766)
5766 / 3 = 1922 (the remainder is 0, so 3 is a divisor of 5766)
...
5766 / 5765 = 1.0001734605377 (the remainder is 1, so 5765 is not a divisor of 5766)
5766 / 5766 = 1 (the remainder is 0, so 5766 is a divisor of 5766)

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 5766 (i.e. 75.934182026279). 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 $\frac{N}{d} = D$ )

5766 / 1 = 5766 (the remainder is 0, so 1 and 5766 are divisors of 5766)
5766 / 2 = 2883 (the remainder is 0, so 2 and 2883 are divisors of 5766)
5766 / 3 = 1922 (the remainder is 0, so 3 and 1922 are divisors of 5766)
...
5766 / 74 = 77.918918918919 (the remainder is 68, so 74 is not a divisor of 5766)
5766 / 75 = 76.88 (the remainder is 66, so 75 is not a divisor of 5766)