Step 1 :
Divide $ 3072 $ by $ 1728 $ and get the remainder

$$ 3072 : 1728 = 1 \text{ ( remainder is } \color{blue}{ 1344 } \text{ ) } $$

The remainder is positive ($ 1344 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1728 $ by $ \color{blue}{ 1344 } $ and get the remainder

$$ 1728 : 1344 = 1 \text{ ( remainder is } \color{blue}{ 384 } \text{ ) } $$

The remainder is still positive ($ 384 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1344 $ by $ \color{blue}{ 384 } $ and get the remainder

$$ 1344 : 384 = 3 \text{ ( remainder is } \color{blue}{ 192 } \text{ ) } $$

The remainder is still positive ($ 192 > 0 $), so we will continue with division.

Step 4 :
Divide $ 384 $ by $ \color{blue}{ 192 } $ and get the remainder

$$ 384 : \color{blue}{ \boxed { 192 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 192 }} $.

This solution can be visualized using a Venn diagram.

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

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