Step 1 :
Divide $ 3921 $ by $ 538 $ and get the remainder

$$ 3921 : 538 = 7 \text{ ( remainder is } \color{blue}{ 155 } \text{ ) } $$

The remainder is positive ($ 155 > 0 $), so we will continue with division.

Step 2 :
Divide $ 538 $ by $ \color{blue}{ 155 } $ and get the remainder

$$ 538 : 155 = 3 \text{ ( remainder is } \color{blue}{ 73 } \text{ ) } $$

The remainder is still positive ($ 73 > 0 $), so we will continue with division.

Step 3 :
Divide $ 155 $ by $ \color{blue}{ 73 } $ and get the remainder

$$ 155 : 73 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 4 :
Divide $ 73 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 73 : 9 = 8 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 5 :
Divide $ 9 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 1 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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