What are the divisors of 5781?

1, 3, 41, 47, 123, 141, 1927, 5781

There is a total of 8 positive divisors.
The sum of these divisors is 8064.
The arithmetic mean is 1008.

8 odd divisors

1, 3, 41, 47, 123, 141, 1927, 5781

How to compute the divisors of 5781?

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 5781 by each of the numbers from 1 to 5781 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)

5781 / 1 = 5781 (the remainder is 0, so 1 is a divisor of 5781)
5781 / 2 = 2890.5 (the remainder is 1, so 2 is not a divisor of 5781)
5781 / 3 = 1927 (the remainder is 0, so 3 is a divisor of 5781)
...
5781 / 5780 = 1.0001730103806 (the remainder is 1, so 5780 is not a divisor of 5781)
5781 / 5781 = 1 (the remainder is 0, so 5781 is a divisor of 5781)

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 5781 (i.e. 76.032887621081). 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 $\frac{N}{d} = D$ )

5781 / 1 = 5781 (the remainder is 0, so 1 and 5781 are divisors of 5781)
5781 / 2 = 2890.5 (the remainder is 1, so 2 is not a divisor of 5781)
5781 / 3 = 1927 (the remainder is 0, so 3 and 1927 are divisors of 5781)
...
5781 / 75 = 77.08 (the remainder is 6, so 75 is not a divisor of 5781)
5781 / 76 = 76.065789473684 (the remainder is 5, so 76 is not a divisor of 5781)