Step 1 :
Divide $ 3921 $ by $ 638 $ and get the remainder

$$ 3921 : 638 = 6 \text{ ( remainder is } \color{blue}{ 93 } \text{ ) } $$

The remainder is positive ($ 93 > 0 $), so we will continue with division.

Step 2 :
Divide $ 638 $ by $ \color{blue}{ 93 } $ and get the remainder

$$ 638 : 93 = 6 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 3 :
Divide $ 93 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 93 : 80 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 4 :
Divide $ 80 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 80 : 13 = 6 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 5 :
Divide $ 13 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 13 : 2 = 6 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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