What are the divisors of 5811?

1, 3, 13, 39, 149, 447, 1937, 5811

There is a total of 8 positive divisors.
The sum of these divisors is 8400.
The arithmetic mean is 1050.

8 odd divisors

1, 3, 13, 39, 149, 447, 1937, 5811

How to compute the divisors of 5811?

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 5811 by each of the numbers from 1 to 5811 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)

5811 / 1 = 5811 (the remainder is 0, so 1 is a divisor of 5811)
5811 / 2 = 2905.5 (the remainder is 1, so 2 is not a divisor of 5811)
5811 / 3 = 1937 (the remainder is 0, so 3 is a divisor of 5811)
...
5811 / 5810 = 1.0001721170396 (the remainder is 1, so 5810 is not a divisor of 5811)
5811 / 5811 = 1 (the remainder is 0, so 5811 is a divisor of 5811)

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 5811 (i.e. 76.229915387596). 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 $\frac{N}{d} = D$ )

5811 / 1 = 5811 (the remainder is 0, so 1 and 5811 are divisors of 5811)
5811 / 2 = 2905.5 (the remainder is 1, so 2 is not a divisor of 5811)
5811 / 3 = 1937 (the remainder is 0, so 3 and 1937 are divisors of 5811)
...
5811 / 75 = 77.48 (the remainder is 36, so 75 is not a divisor of 5811)
5811 / 76 = 76.460526315789 (the remainder is 35, so 76 is not a divisor of 5811)