Step 1 :
Divide $ 6183 $ by $ 1518 $ and get the remainder

$$ 6183 : 1518 = 4 \text{ ( remainder is } \color{blue}{ 111 } \text{ ) } $$

The remainder is positive ($ 111 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 111 } $ and get the remainder

$$ 1518 : 111 = 13 \text{ ( remainder is } \color{blue}{ 75 } \text{ ) } $$

The remainder is still positive ($ 75 > 0 $), so we will continue with division.

Step 3 :
Divide $ 111 $ by $ \color{blue}{ 75 } $ and get the remainder

$$ 111 : 75 = 1 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is still positive ($ 36 > 0 $), so we will continue with division.

Step 4 :
Divide $ 75 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 75 : 36 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 5 :
Divide $ 36 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 36 : \color{blue}{ \boxed { 3 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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