Step 1 :
Divide $ 128 $ by $ 54 $ and get the remainder

$$ 128 : 54 = 2 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is positive ($ 20 > 0 $), so we will continue with division.

Step 2 :
Divide $ 54 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 54 : 20 = 2 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 3 :
Divide $ 20 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 20 : 14 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 4 :
Divide $ 14 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 14 : 6 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder

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

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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