What are the divisors of 2711?

1, 2711

There is a total of 2 positive divisors.
The sum of these divisors is 2712.
The arithmetic mean is 1356.

2 odd divisors

1, 2711

How to compute the divisors of 2711?

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 2711 by each of the numbers from 1 to 2711 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)

2711 / 1 = 2711 (the remainder is 0, so 1 is a divisor of 2711)
2711 / 2 = 1355.5 (the remainder is 1, so 2 is not a divisor of 2711)
2711 / 3 = 903.66666666667 (the remainder is 2, so 3 is not a divisor of 2711)
...
2711 / 2710 = 1.00036900369 (the remainder is 1, so 2710 is not a divisor of 2711)
2711 / 2711 = 1 (the remainder is 0, so 2711 is a divisor of 2711)

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 2711 (i.e. 52.067264187779). 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 $\frac{N}{d} = D$ )

2711 / 1 = 2711 (the remainder is 0, so 1 and 2711 are divisors of 2711)
2711 / 2 = 1355.5 (the remainder is 1, so 2 is not a divisor of 2711)
2711 / 3 = 903.66666666667 (the remainder is 2, so 3 is not a divisor of 2711)
...
2711 / 51 = 53.156862745098 (the remainder is 8, so 51 is not a divisor of 2711)
2711 / 52 = 52.134615384615 (the remainder is 7, so 52 is not a divisor of 2711)