The GCD of given numbers is 66666.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}6666600000 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot5\cdot5\cdot5\cdot5\cdot41\cdot271\\[8pt]6666666666 =& 2\cdot3\cdot11\cdot41\cdot271\cdot9091\\[8pt]\end{aligned}$$(view steps on how to factor 6666600000 and 6666666666. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}6666600000 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot2\cdot\color{red}{\boxed{3}}\cdot5\cdot5\cdot5\cdot5\cdot5\cdot\color{Fuchsia}{\boxed{41}}\cdot\color{Orange}{\boxed{271}}\\[8pt]6666666666 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot11\cdot\color{Fuchsia}{\boxed{41}}\cdot\color{Orange}{\boxed{271}}\cdot9091\\[8pt]\end{aligned}$$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.