Step 1 :
Divide $ 450 $ by $ 270 $ and get the remainder

$$ 450 : 270 = 1 \text{ ( remainder is } \color{blue}{ 180 } \text{ ) } $$

The remainder is positive ($ 180 > 0 $), so we will continue with division.

Step 2 :
Divide $ 270 $ by $ \color{blue}{ 180 } $ and get the remainder

$$ 270 : 180 = 1 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 3 :
Divide $ 180 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 180 : \color{blue}{ \boxed { 90 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 90 }} $.

This solution can be visualized using a Venn diagram.

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

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