Step 1 :
Divide $ 3621 $ by $ 1938 $ and get the remainder

$$ 3621 : 1938 = 1 \text{ ( remainder is } \color{blue}{ 1683 } \text{ ) } $$

The remainder is positive ($ 1683 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1938 $ by $ \color{blue}{ 1683 } $ and get the remainder

$$ 1938 : 1683 = 1 \text{ ( remainder is } \color{blue}{ 255 } \text{ ) } $$

The remainder is still positive ($ 255 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1683 $ by $ \color{blue}{ 255 } $ and get the remainder

$$ 1683 : 255 = 6 \text{ ( remainder is } \color{blue}{ 153 } \text{ ) } $$

The remainder is still positive ($ 153 > 0 $), so we will continue with division.

Step 4 :
Divide $ 255 $ by $ \color{blue}{ 153 } $ and get the remainder

$$ 255 : 153 = 1 \text{ ( remainder is } \color{blue}{ 102 } \text{ ) } $$

The remainder is still positive ($ 102 > 0 $), so we will continue with division.

Step 5 :
Divide $ 153 $ by $ \color{blue}{ 102 } $ and get the remainder

$$ 153 : 102 = 1 \text{ ( remainder is } \color{blue}{ 51 } \text{ ) } $$

The remainder is still positive ($ 51 > 0 $), so we will continue with division.

Step 6 :
Divide $ 102 $ by $ \color{blue}{ 51 } $ and get the remainder

$$ 102 : \color{blue}{ \boxed { 51 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 51 }} $.

This solution can be visualized using a Venn diagram.

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

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