The GCD of given numbers is 68.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}7684 =& 2\cdot2\cdot17\cdot113\\[8pt]4148 =& 2\cdot2\cdot17\cdot61\\[8pt]\end{aligned}$$(view steps on how to factor 7684 and 4148. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}7684 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{17}}\cdot113\\[8pt]4148 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{17}}\cdot61\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot2\cdot17 = 68 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.