Step 1 : Find prime factorization of each number.

$$\begin{aligned}372997709 =& 7\cdot1759\cdot30293\\[8pt]227558538 =& 2\cdot3\cdot3\cdot3\cdot31\cdot135937\\[8pt]\end{aligned}$$

(view steps on how to factor 372997709 and 227558538. )

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

$$\begin{aligned}372997709 =& 7\cdot1759\cdot30293\\[8pt]227558538 =& 2\cdot3\cdot3\cdot3\cdot31\cdot135937\\[8pt]\end{aligned}$$

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator