Step 1 :
Divide $ 2394 $ by $ 1638 $ and get the remainder

$$ 2394 : 1638 = 1 \text{ ( remainder is } \color{blue}{ 756 } \text{ ) } $$

The remainder is positive ($ 756 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1638 $ by $ \color{blue}{ 756 } $ and get the remainder

$$ 1638 : 756 = 2 \text{ ( remainder is } \color{blue}{ 126 } \text{ ) } $$

The remainder is still positive ($ 126 > 0 $), so we will continue with division.

Step 3 :
Divide $ 756 $ by $ \color{blue}{ 126 } $ and get the remainder

$$ 756 : \color{blue}{ \boxed { 126 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 126 }} $.

This solution can be visualized using a Venn diagram.

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

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