Step 1 :
Divide $ 1296 $ by $ 384 $ and get the remainder

$$ 1296 : 384 = 3 \text{ ( remainder is } \color{blue}{ 144 } \text{ ) } $$

The remainder is positive ($ 144 > 0 $), so we will continue with division.

Step 2 :
Divide $ 384 $ by $ \color{blue}{ 144 } $ and get the remainder

$$ 384 : 144 = 2 \text{ ( remainder is } \color{blue}{ 96 } \text{ ) } $$

The remainder is still positive ($ 96 > 0 $), so we will continue with division.

Step 3 :
Divide $ 144 $ by $ \color{blue}{ 96 } $ and get the remainder

$$ 144 : 96 = 1 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 4 :
Divide $ 96 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 96 : \color{blue}{ \boxed { 48 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 48 }} $.

This solution can be visualized using a Venn diagram.

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

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