What are the divisors of 2871?

1, 3, 9, 11, 29, 33, 87, 99, 261, 319, 957, 2871

There is a total of 12 positive divisors.
The sum of these divisors is 4680.
The arithmetic mean is 390.

12 odd divisors

1, 3, 9, 11, 29, 33, 87, 99, 261, 319, 957, 2871

How to compute the divisors of 2871?

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 2871 by each of the numbers from 1 to 2871 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)

2871 / 1 = 2871 (the remainder is 0, so 1 is a divisor of 2871)
2871 / 2 = 1435.5 (the remainder is 1, so 2 is not a divisor of 2871)
2871 / 3 = 957 (the remainder is 0, so 3 is a divisor of 2871)
...
2871 / 2870 = 1.0003484320557 (the remainder is 1, so 2870 is not a divisor of 2871)
2871 / 2871 = 1 (the remainder is 0, so 2871 is a divisor of 2871)

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 2871 (i.e. 53.581713298475). 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 $\frac{N}{d} = D$ )

2871 / 1 = 2871 (the remainder is 0, so 1 and 2871 are divisors of 2871)
2871 / 2 = 1435.5 (the remainder is 1, so 2 is not a divisor of 2871)
2871 / 3 = 957 (the remainder is 0, so 3 and 957 are divisors of 2871)
...
2871 / 52 = 55.211538461538 (the remainder is 11, so 52 is not a divisor of 2871)
2871 / 53 = 54.169811320755 (the remainder is 9, so 53 is not a divisor of 2871)