The GCD of given numbers is 82.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}410 =& 2\cdot5\cdot41\\[8pt]1394 =& 2\cdot17\cdot41\\[8pt]3034 =& 2\cdot37\cdot41\\[8pt]\end{aligned}$$(view steps on how to factor 410, 1394 and 3034. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}410 =& \color{blue}{\boxed{2}}\cdot5\cdot\color{red}{\boxed{41}}\\[8pt]1394 =& \color{blue}{\boxed{2}}\cdot17\cdot\color{red}{\boxed{41}}\\[8pt]3034 =& \color{blue}{\boxed{2}}\cdot37\cdot\color{red}{\boxed{41}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot41 = 82 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.