Step 1 :
Divide $ 221 $ by $ 153 $ and get the remainder

$$ 221 : 153 = 1 \text{ ( remainder is } \color{blue}{ 68 } \text{ ) } $$

The remainder is positive ($ 68 > 0 $), so we will continue with division.

Step 2 :
Divide $ 153 $ by $ \color{blue}{ 68 } $ and get the remainder

$$ 153 : 68 = 2 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 3 :
Divide $ 68 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 68 : \color{blue}{ \boxed { 17 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.

This solution can be visualized using a Venn diagram.

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

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