The GCD of given numbers is 2.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}1970 =& 2\cdot5\cdot197\\[8pt]1066 =& 2\cdot13\cdot41\\[8pt]\end{aligned}$$(view steps on how to factor 1970 and 1066. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}1970 =& \color{blue}{\boxed{2}}\cdot5\cdot197\\[8pt]1066 =& \color{blue}{\boxed{2}}\cdot13\cdot41\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 2 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.