Step 1 : Find prime factorization of each number.

$$\begin{aligned}8466 =& 2\cdot3\cdot17\cdot83\\[8pt]7684 =& 2\cdot2\cdot17\cdot113\\[8pt]\end{aligned}$$

(view steps on how to factor 8466 and 7684. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}8466 =& \color{blue}{\boxed{2}}\cdot3\cdot\color{red}{\boxed{17}}\cdot83\\[8pt]7684 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{17}}\cdot113\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot17 = 34 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator