Step 1 :
Divide $ 327 $ by $ 180 $ and get the remainder

$$ 327 : 180 = 1 \text{ ( remainder is } \color{blue}{ 147 } \text{ ) } $$

The remainder is positive ($ 147 > 0 $), so we will continue with division.

Step 2 :
Divide $ 180 $ by $ \color{blue}{ 147 } $ and get the remainder

$$ 180 : 147 = 1 \text{ ( remainder is } \color{blue}{ 33 } \text{ ) } $$

The remainder is still positive ($ 33 > 0 $), so we will continue with division.

Step 3 :
Divide $ 147 $ by $ \color{blue}{ 33 } $ and get the remainder

$$ 147 : 33 = 4 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 4 :
Divide $ 33 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 33 : 15 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 5 :
Divide $ 15 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 15 : \color{blue}{ \boxed { 3 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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