Step 1 :
Divide $ 924 $ by $ 189 $ and get the remainder

$$ 924 : 189 = 4 \text{ ( remainder is } \color{blue}{ 168 } \text{ ) } $$

The remainder is positive ($ 168 > 0 $), so we will continue with division.

Step 2 :
Divide $ 189 $ by $ \color{blue}{ 168 } $ and get the remainder

$$ 189 : 168 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 3 :
Divide $ 168 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 168 : \color{blue}{ \boxed { 21 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 21 }} $.

This solution can be visualized using a Venn diagram.

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

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