Step 1 : Find prime factorization of each number.

$$\begin{aligned}704 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot11\\[8pt]22 =& 2\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 704 and 22. )

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

$$\begin{aligned}704 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot2\cdot\color{red}{\boxed{11}}\\[8pt]22 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{11}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot11 = 22 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator