What are the divisors of 5787?

1, 3, 9, 643, 1929, 5787

There is a total of 6 positive divisors.
The sum of these divisors is 8372.
The arithmetic mean is 1395.3333333333.

6 odd divisors

1, 3, 9, 643, 1929, 5787

How to compute the divisors of 5787?

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 5787 by each of the numbers from 1 to 5787 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)

5787 / 1 = 5787 (the remainder is 0, so 1 is a divisor of 5787)
5787 / 2 = 2893.5 (the remainder is 1, so 2 is not a divisor of 5787)
5787 / 3 = 1929 (the remainder is 0, so 3 is a divisor of 5787)
...
5787 / 5786 = 1.0001728309713 (the remainder is 1, so 5786 is not a divisor of 5787)
5787 / 5787 = 1 (the remainder is 0, so 5787 is a divisor of 5787)

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 5787 (i.e. 76.072333998636). 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 $\frac{N}{d} = D$ )

5787 / 1 = 5787 (the remainder is 0, so 1 and 5787 are divisors of 5787)
5787 / 2 = 2893.5 (the remainder is 1, so 2 is not a divisor of 5787)
5787 / 3 = 1929 (the remainder is 0, so 3 and 1929 are divisors of 5787)
...
5787 / 75 = 77.16 (the remainder is 12, so 75 is not a divisor of 5787)
5787 / 76 = 76.144736842105 (the remainder is 11, so 76 is not a divisor of 5787)