Step 1 : Find prime factorization of each number.

$$\begin{aligned}1746 =& 2\cdot3\cdot3\cdot97\\[8pt]28324 =& 2\cdot2\cdot73\cdot97\\[8pt]\end{aligned}$$

(view steps on how to factor 1746 and 28324. )

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

$$\begin{aligned}1746 =& \color{blue}{\boxed{2}}\cdot3\cdot3\cdot\color{red}{\boxed{97}}\\[8pt]28324 =& \color{blue}{\boxed{2}}\cdot2\cdot73\cdot\color{red}{\boxed{97}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot97 = 194 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator