Step 1 :
Divide $ 612 $ by $ 429 $ and get the remainder

$$ 612 : 429 = 1 \text{ ( remainder is } \color{blue}{ 183 } \text{ ) } $$

The remainder is positive ($ 183 > 0 $), so we will continue with division.

Step 2 :
Divide $ 429 $ by $ \color{blue}{ 183 } $ and get the remainder

$$ 429 : 183 = 2 \text{ ( remainder is } \color{blue}{ 63 } \text{ ) } $$

The remainder is still positive ($ 63 > 0 $), so we will continue with division.

Step 3 :
Divide $ 183 $ by $ \color{blue}{ 63 } $ and get the remainder

$$ 183 : 63 = 2 \text{ ( remainder is } \color{blue}{ 57 } \text{ ) } $$

The remainder is still positive ($ 57 > 0 $), so we will continue with division.

Step 4 :
Divide $ 63 $ by $ \color{blue}{ 57 } $ and get the remainder

$$ 63 : 57 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 5 :
Divide $ 57 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 57 : 6 = 9 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 6 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 3 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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