Step 1 : Find prime factorization of each number.

$$\begin{aligned}32307250 =& 2\cdot5\cdot5\cdot5\cdot129229\\[8pt]5889578772 =& 2\cdot2\cdot3\cdot7\cdot11\cdot31\cdot127\cdot1619\\[8pt]\end{aligned}$$

(view steps on how to factor 32307250 and 5889578772. )

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

$$\begin{aligned}32307250 =& \color{blue}{\boxed{2}}\cdot5\cdot5\cdot5\cdot129229\\[8pt]5889578772 =& \color{blue}{\boxed{2}}\cdot2\cdot3\cdot7\cdot11\cdot31\cdot127\cdot1619\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator