Step 1 : Find prime factorization of each number.

$$\begin{aligned}3234 =& 2\cdot3\cdot7\cdot7\cdot11\\[8pt]2541 =& 3\cdot7\cdot11\cdot11\\[8pt]6006 =& 2\cdot3\cdot7\cdot11\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 3234, 2541 and 6006. )

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

$$\begin{aligned}3234 =& 2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{7}}\cdot7\cdot\color{Fuchsia}{\boxed{11}}\\[8pt]2541 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{11}}\cdot11\\[8pt]6006 =& 2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{7}}\cdot\color{Fuchsia}{\boxed{11}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot7\cdot11 = 231 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator