What are the divisors of 5788?

1, 2, 4, 1447, 2894, 5788

There is a total of 6 positive divisors.
The sum of these divisors is 10136.
The arithmetic mean is 1689.3333333333.

4 even divisors

2, 4, 2894, 5788

2 odd divisors

1, 1447

How to compute the divisors of 5788?

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 5788 by each of the numbers from 1 to 5788 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)

5788 / 1 = 5788 (the remainder is 0, so 1 is a divisor of 5788)
5788 / 2 = 2894 (the remainder is 0, so 2 is a divisor of 5788)
5788 / 3 = 1929.3333333333 (the remainder is 1, so 3 is not a divisor of 5788)
...
5788 / 5787 = 1.0001728011059 (the remainder is 1, so 5787 is not a divisor of 5788)
5788 / 5788 = 1 (the remainder is 0, so 5788 is a divisor of 5788)

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 5788 (i.e. 76.078906406441). 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 $\frac{N}{d} = D$ )

5788 / 1 = 5788 (the remainder is 0, so 1 and 5788 are divisors of 5788)
5788 / 2 = 2894 (the remainder is 0, so 2 and 2894 are divisors of 5788)
5788 / 3 = 1929.3333333333 (the remainder is 1, so 3 is not a divisor of 5788)
...
5788 / 75 = 77.173333333333 (the remainder is 13, so 75 is not a divisor of 5788)
5788 / 76 = 76.157894736842 (the remainder is 12, so 76 is not a divisor of 5788)