The GCD of given numbers is 9.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}117 =& 3\cdot3\cdot13\\[8pt]4113 =& 3\cdot3\cdot457\\[8pt]\end{aligned}$$(view steps on how to factor 117 and 4113. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}117 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot13\\[8pt]4113 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot457\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3\cdot3 = 9 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.