Step 1 :
Divide $ 344 $ by $ 342 $ and get the remainder

$$ 344 : 342 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is positive ($ 2 > 0 $), so we will continue with division.

Step 2 :
Divide $ 342 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 342 : \color{blue}{ \boxed { 2 }} = 171 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator