Step 1 :
Divide $ 657 $ by $ 306 $ and get the remainder

$$ 657 : 306 = 2 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is positive ($ 45 > 0 $), so we will continue with division.

Step 2 :
Divide $ 306 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 306 : 45 = 6 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is still positive ($ 36 > 0 $), so we will continue with division.

Step 3 :
Divide $ 45 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 45 : 36 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

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

Step 4 :
Divide $ 36 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 36 : \color{blue}{ \boxed { 9 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.

This solution can be visualized using a Venn diagram.

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

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