Step 1 : Find prime factorization of each number.

$$\begin{aligned}82472 =& 2\cdot2\cdot2\cdot13\cdot13\cdot61\\[8pt]79300 =& 2\cdot2\cdot5\cdot5\cdot13\cdot61\\[8pt]\end{aligned}$$

(view steps on how to factor 82472 and 79300. )

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

$$\begin{aligned}82472 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{13}}\cdot13\cdot\color{Orange}{\boxed{61}}\\[8pt]79300 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot5\cdot5\cdot\color{Fuchsia}{\boxed{13}}\cdot\color{Orange}{\boxed{61}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot13\cdot61 = 3172 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator