The GCD of given numbers is 267.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}534 =& 2\cdot3\cdot89\\[8pt]801 =& 3\cdot3\cdot89\\[8pt]1335 =& 3\cdot5\cdot89\\[8pt]\end{aligned}$$(view steps on how to factor 534, 801 and 1335. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}534 =& 2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{89}}\\[8pt]801 =& \color{blue}{\boxed{3}}\cdot3\cdot\color{red}{\boxed{89}}\\[8pt]1335 =& \color{blue}{\boxed{3}}\cdot5\cdot\color{red}{\boxed{89}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3\cdot89 = 267 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.