Step 1 : Find prime factorization of each number.

$$\begin{aligned}78912 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot137\\[8pt]83159 =& 137\cdot607\\[8pt]\end{aligned}$$

(view steps on how to factor 78912 and 83159. )

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

$$\begin{aligned}78912 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot\color{blue}{\boxed{137}}\\[8pt]83159 =& \color{blue}{\boxed{137}}\cdot607\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 137 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator