What are the divisors of 2717?

1, 11, 13, 19, 143, 209, 247, 2717

There is a total of 8 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 420.

8 odd divisors

1, 11, 13, 19, 143, 209, 247, 2717

How to compute the divisors of 2717?

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 2717 by each of the numbers from 1 to 2717 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)

2717 / 1 = 2717 (the remainder is 0, so 1 is a divisor of 2717)
2717 / 2 = 1358.5 (the remainder is 1, so 2 is not a divisor of 2717)
2717 / 3 = 905.66666666667 (the remainder is 2, so 3 is not a divisor of 2717)
...
2717 / 2716 = 1.0003681885125 (the remainder is 1, so 2716 is not a divisor of 2717)
2717 / 2717 = 1 (the remainder is 0, so 2717 is a divisor of 2717)

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 2717 (i.e. 52.124850119689). 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 $\frac{N}{d} = D$ )

2717 / 1 = 2717 (the remainder is 0, so 1 and 2717 are divisors of 2717)
2717 / 2 = 1358.5 (the remainder is 1, so 2 is not a divisor of 2717)
2717 / 3 = 905.66666666667 (the remainder is 2, so 3 is not a divisor of 2717)
...
2717 / 51 = 53.274509803922 (the remainder is 14, so 51 is not a divisor of 2717)
2717 / 52 = 52.25 (the remainder is 13, so 52 is not a divisor of 2717)