Step 1 : Find prime factorization of each number.

$$\begin{aligned}53963 =& 7\cdot13\cdot593\\[8pt]42042 =& 2\cdot3\cdot7\cdot7\cdot11\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 53963 and 42042. )

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

$$\begin{aligned}53963 =& \color{blue}{\boxed{7}}\cdot\color{red}{\boxed{13}}\cdot593\\[8pt]42042 =& 2\cdot3\cdot\color{blue}{\boxed{7}}\cdot7\cdot11\cdot\color{red}{\boxed{13}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 7\cdot13 = 91 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator