What are the divisors of 5768?

1, 2, 4, 7, 8, 14, 28, 56, 103, 206, 412, 721, 824, 1442, 2884, 5768

There is a total of 16 positive divisors.
The sum of these divisors is 12480.
The arithmetic mean is 780.

12 even divisors

2, 4, 8, 14, 28, 56, 206, 412, 824, 1442, 2884, 5768

4 odd divisors

1, 7, 103, 721

How to compute the divisors of 5768?

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 5768 by each of the numbers from 1 to 5768 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)

5768 / 1 = 5768 (the remainder is 0, so 1 is a divisor of 5768)
5768 / 2 = 2884 (the remainder is 0, so 2 is a divisor of 5768)
5768 / 3 = 1922.6666666667 (the remainder is 2, so 3 is not a divisor of 5768)
...
5768 / 5767 = 1.0001734003815 (the remainder is 1, so 5767 is not a divisor of 5768)
5768 / 5768 = 1 (the remainder is 0, so 5768 is a divisor of 5768)

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 5768 (i.e. 75.94735018419). 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 $\frac{N}{d} = D$ )

5768 / 1 = 5768 (the remainder is 0, so 1 and 5768 are divisors of 5768)
5768 / 2 = 2884 (the remainder is 0, so 2 and 2884 are divisors of 5768)
5768 / 3 = 1922.6666666667 (the remainder is 2, so 3 is not a divisor of 5768)
...
5768 / 74 = 77.945945945946 (the remainder is 70, so 74 is not a divisor of 5768)
5768 / 75 = 76.906666666667 (the remainder is 68, so 75 is not a divisor of 5768)