What are the divisors of 2811?

1, 3, 937, 2811

There is a total of 4 positive divisors.
The sum of these divisors is 3752.
The arithmetic mean is 938.

4 odd divisors

1, 3, 937, 2811

How to compute the divisors of 2811?

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 2811 by each of the numbers from 1 to 2811 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)

2811 / 1 = 2811 (the remainder is 0, so 1 is a divisor of 2811)
2811 / 2 = 1405.5 (the remainder is 1, so 2 is not a divisor of 2811)
2811 / 3 = 937 (the remainder is 0, so 3 is a divisor of 2811)
...
2811 / 2810 = 1.0003558718861 (the remainder is 1, so 2810 is not a divisor of 2811)
2811 / 2811 = 1 (the remainder is 0, so 2811 is a divisor of 2811)

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 2811 (i.e. 53.018864567246). 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 $\frac{N}{d} = D$ )

2811 / 1 = 2811 (the remainder is 0, so 1 and 2811 are divisors of 2811)
2811 / 2 = 1405.5 (the remainder is 1, so 2 is not a divisor of 2811)
2811 / 3 = 937 (the remainder is 0, so 3 and 937 are divisors of 2811)
...
2811 / 52 = 54.057692307692 (the remainder is 3, so 52 is not a divisor of 2811)
2811 / 53 = 53.037735849057 (the remainder is 2, so 53 is not a divisor of 2811)