The GCD of given numbers is 79.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}6952 =& 2\cdot2\cdot2\cdot11\cdot79\\[8pt]7189 =& 7\cdot13\cdot79\\[8pt]\end{aligned}$$(view steps on how to factor 6952 and 7189. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}6952 =& 2\cdot2\cdot2\cdot11\cdot\color{blue}{\boxed{79}}\\[8pt]7189 =& 7\cdot13\cdot\color{blue}{\boxed{79}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 79 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.