Step 1 : Find prime factorization of each number.

$$\begin{aligned}66852 =& 2\cdot2\cdot3\cdot3\cdot3\cdot619\\[8pt]575000000 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 66852 and 575000000. )

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

$$\begin{aligned}66852 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot3\cdot3\cdot3\cdot619\\[8pt]575000000 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot5\cdot23\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2 = 4 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator