The GCD of given numbers is 3.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}12327 =& 3\cdot7\cdot587\\[8pt]2409 =& 3\cdot11\cdot73\\[8pt]\end{aligned}$$(view steps on how to factor 12327 and 2409. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}12327 =& \color{blue}{\boxed{3}}\cdot7\cdot587\\[8pt]2409 =& \color{blue}{\boxed{3}}\cdot11\cdot73\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.