Step 1 : Find prime factorization of each number.

$$\begin{aligned}6064 =& 2\cdot2\cdot2\cdot2\cdot379\\[8pt]2768 =& 2\cdot2\cdot2\cdot2\cdot173\\[8pt]\end{aligned}$$

(view steps on how to factor 6064 and 2768. )

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

$$\begin{aligned}6064 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot379\\[8pt]2768 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot173\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2 = 16 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator