Step 1 : Find prime factorization of each number.

$$\begin{aligned}696 =& 2\cdot2\cdot2\cdot3\cdot29\\[8pt]148 =& 2\cdot2\cdot37\\[8pt]198 =& 2\cdot3\cdot3\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 696, 148 and 198. )

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

$$\begin{aligned}696 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot3\cdot29\\[8pt]148 =& \color{blue}{\boxed{2}}\cdot2\cdot37\\[8pt]198 =& \color{blue}{\boxed{2}}\cdot3\cdot3\cdot11\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator