Step 1 :
Divide $ 1149 $ by $ 201 $ and get the remainder

$$ 1149 : 201 = 5 \text{ ( remainder is } \color{blue}{ 144 } \text{ ) } $$

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

Step 2 :
Divide $ 201 $ by $ \color{blue}{ 144 } $ and get the remainder

$$ 201 : 144 = 1 \text{ ( remainder is } \color{blue}{ 57 } \text{ ) } $$

The remainder is still positive ($ 57 > 0 $), so we will continue with division.

Step 3 :
Divide $ 144 $ by $ \color{blue}{ 57 } $ and get the remainder

$$ 144 : 57 = 2 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 4 :
Divide $ 57 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 57 : 30 = 1 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 5 :
Divide $ 30 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 30 : 27 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 6 :
Divide $ 27 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 27 : \color{blue}{ \boxed { 3 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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