Step 1 : Find prime factorization of each number.

$$\begin{aligned}3927473 =& 11\cdot67\cdot73\cdot73\\[8pt]82709 =& 11\cdot73\cdot103\\[8pt]1210121 =& 11\cdot11\cdot73\cdot137\\[8pt]\end{aligned}$$

(view steps on how to factor 3927473, 82709 and 1210121. )

Step 2 : Put a box around factors that are common for all numbers:

$$\begin{aligned}3927473 =& \color{blue}{\boxed{11}}\cdot67\cdot\color{red}{\boxed{73}}\cdot73\\[8pt]82709 =& \color{blue}{\boxed{11}}\cdot\color{red}{\boxed{73}}\cdot103\\[8pt]1210121 =& \color{blue}{\boxed{11}}\cdot11\cdot\color{red}{\boxed{73}}\cdot137\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 11\cdot73 = 803 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator