Step 1 :
Divide $ 528 $ by $ 324 $ and get the remainder

$$ 528 : 324 = 1 \text{ ( remainder is } \color{blue}{ 204 } \text{ ) } $$

The remainder is positive ($ 204 > 0 $), so we will continue with division.

Step 2 :
Divide $ 324 $ by $ \color{blue}{ 204 } $ and get the remainder

$$ 324 : 204 = 1 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 3 :
Divide $ 204 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 204 : 120 = 1 \text{ ( remainder is } \color{blue}{ 84 } \text{ ) } $$

The remainder is still positive ($ 84 > 0 $), so we will continue with division.

Step 4 :
Divide $ 120 $ by $ \color{blue}{ 84 } $ and get the remainder

$$ 120 : 84 = 1 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

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

Step 5 :
Divide $ 84 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 84 : 36 = 2 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 6 :
Divide $ 36 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 36 : \color{blue}{ \boxed { 12 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.

This solution can be visualized using a Venn diagram.

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

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