Step 1 : Find prime factorization of each number.

$$\begin{aligned}171 =& 3\cdot3\cdot19\\[8pt]399 =& 3\cdot7\cdot19\\[8pt]741 =& 3\cdot13\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 171, 399 and 741. )

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

$$\begin{aligned}171 =& \color{blue}{\boxed{3}}\cdot3\cdot\color{red}{\boxed{19}}\\[8pt]399 =& \color{blue}{\boxed{3}}\cdot7\cdot\color{red}{\boxed{19}}\\[8pt]741 =& \color{blue}{\boxed{3}}\cdot13\cdot\color{red}{\boxed{19}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot19 = 57 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator