What are the divisors of 2771?

1, 17, 163, 2771

There is a total of 4 positive divisors.
The sum of these divisors is 2952.
The arithmetic mean is 738.

4 odd divisors

1, 17, 163, 2771

How to compute the divisors of 2771?

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 2771 by each of the numbers from 1 to 2771 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)

2771 / 1 = 2771 (the remainder is 0, so 1 is a divisor of 2771)
2771 / 2 = 1385.5 (the remainder is 1, so 2 is not a divisor of 2771)
2771 / 3 = 923.66666666667 (the remainder is 2, so 3 is not a divisor of 2771)
...
2771 / 2770 = 1.0003610108303 (the remainder is 1, so 2770 is not a divisor of 2771)
2771 / 2771 = 1 (the remainder is 0, so 2771 is a divisor of 2771)

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 2771 (i.e. 52.640288753007). 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 $\frac{N}{d} = D$ )

2771 / 1 = 2771 (the remainder is 0, so 1 and 2771 are divisors of 2771)
2771 / 2 = 1385.5 (the remainder is 1, so 2 is not a divisor of 2771)
2771 / 3 = 923.66666666667 (the remainder is 2, so 3 is not a divisor of 2771)
...
2771 / 51 = 54.333333333333 (the remainder is 17, so 51 is not a divisor of 2771)
2771 / 52 = 53.288461538462 (the remainder is 15, so 52 is not a divisor of 2771)