Step 1 :
Divide $ 36243 $ by $ 4866 $ and get the remainder

$$ 36243 : 4866 = 7 \text{ ( remainder is } \color{blue}{ 2181 } \text{ ) } $$

The remainder is positive ($ 2181 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4866 $ by $ \color{blue}{ 2181 } $ and get the remainder

$$ 4866 : 2181 = 2 \text{ ( remainder is } \color{blue}{ 504 } \text{ ) } $$

The remainder is still positive ($ 504 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2181 $ by $ \color{blue}{ 504 } $ and get the remainder

$$ 2181 : 504 = 4 \text{ ( remainder is } \color{blue}{ 165 } \text{ ) } $$

The remainder is still positive ($ 165 > 0 $), so we will continue with division.

Step 4 :
Divide $ 504 $ by $ \color{blue}{ 165 } $ and get the remainder

$$ 504 : 165 = 3 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 165 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 165 : 9 = 18 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 6 :
Divide $ 9 $ by $ \color{blue}{ 3 } $ and get the remainder

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

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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