The GCD of given numbers is 7.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}910 =& 2\cdot5\cdot7\cdot13\\[8pt]6517 =& 7\cdot7\cdot7\cdot19\\[8pt]\end{aligned}$$(view steps on how to factor 910 and 6517. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}910 =& 2\cdot5\cdot\color{blue}{\boxed{7}}\cdot13\\[8pt]6517 =& \color{blue}{\boxed{7}}\cdot7\cdot7\cdot19\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 7 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.