Step 1 :
Divide $ 12327 $ by $ 2409 $ and get the remainder

$$ 12327 : 2409 = 5 \text{ ( remainder is } \color{blue}{ 282 } \text{ ) } $$

The remainder is positive ($ 282 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2409 $ by $ \color{blue}{ 282 } $ and get the remainder

$$ 2409 : 282 = 8 \text{ ( remainder is } \color{blue}{ 153 } \text{ ) } $$

The remainder is still positive ($ 153 > 0 $), so we will continue with division.

Step 3 :
Divide $ 282 $ by $ \color{blue}{ 153 } $ and get the remainder

$$ 282 : 153 = 1 \text{ ( remainder is } \color{blue}{ 129 } \text{ ) } $$

The remainder is still positive ($ 129 > 0 $), so we will continue with division.

Step 4 :
Divide $ 153 $ by $ \color{blue}{ 129 } $ and get the remainder

$$ 153 : 129 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 5 :
Divide $ 129 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 129 : 24 = 5 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

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

Step 6 :
Divide $ 24 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 24 : 9 = 2 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 7 :
Divide $ 9 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 9 : 6 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 8 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 3 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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