The GCD of given numbers is 66666.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1348119852 =& 2\cdot2\cdot3\cdot41\cdot271\cdot10111\\[8pt]1340719926 =& 2\cdot3\cdot7\cdot13\cdot13\cdot17\cdot41\cdot271\\[8pt]\end{aligned}$$(view steps on how to factor 1348119852 and 1340719926. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1348119852 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{41}}\cdot\color{Orange}{\boxed{271}}\cdot10111\\[8pt]1340719926 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot7\cdot13\cdot13\cdot17\cdot\color{Fuchsia}{\boxed{41}}\cdot\color{Orange}{\boxed{271}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2\cdot3\cdot41\cdot271 = 66666 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.