What are the divisors of 5756?

1, 2, 4, 1439, 2878, 5756

There is a total of 6 positive divisors.
The sum of these divisors is 10080.
The arithmetic mean is 1680.

4 even divisors

2, 4, 2878, 5756

2 odd divisors

1, 1439

How to compute the divisors of 5756?

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 5756 by each of the numbers from 1 to 5756 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)

5756 / 1 = 5756 (the remainder is 0, so 1 is a divisor of 5756)
5756 / 2 = 2878 (the remainder is 0, so 2 is a divisor of 5756)
5756 / 3 = 1918.6666666667 (the remainder is 2, so 3 is not a divisor of 5756)
...
5756 / 5755 = 1.0001737619461 (the remainder is 1, so 5755 is not a divisor of 5756)
5756 / 5756 = 1 (the remainder is 0, so 5756 is a divisor of 5756)

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 5756 (i.e. 75.868306953563). 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 $\frac{N}{d} = D$ )

5756 / 1 = 5756 (the remainder is 0, so 1 and 5756 are divisors of 5756)
5756 / 2 = 2878 (the remainder is 0, so 2 and 2878 are divisors of 5756)
5756 / 3 = 1918.6666666667 (the remainder is 2, so 3 is not a divisor of 5756)
...
5756 / 74 = 77.783783783784 (the remainder is 58, so 74 is not a divisor of 5756)
5756 / 75 = 76.746666666667 (the remainder is 56, so 75 is not a divisor of 5756)