The GCD of given numbers is 89.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}267 =& 3\cdot89\\[8pt]445 =& 5\cdot89\\[8pt]712 =& 2\cdot2\cdot2\cdot89\\[8pt]\end{aligned}$$(view steps on how to factor 267, 445 and 712. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}267 =& 3\cdot\color{blue}{\boxed{89}}\\[8pt]445 =& 5\cdot\color{blue}{\boxed{89}}\\[8pt]712 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{89}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 89 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.