Step 1 : Find prime factorization of each number.

$$\begin{aligned}286 =& 2\cdot11\cdot13\\[8pt]385 =& 5\cdot7\cdot11\\[8pt]418 =& 2\cdot11\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 286, 385 and 418. )

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

$$\begin{aligned}286 =& 2\cdot\color{blue}{\boxed{11}}\cdot13\\[8pt]385 =& 5\cdot7\cdot\color{blue}{\boxed{11}}\\[8pt]418 =& 2\cdot\color{blue}{\boxed{11}}\cdot19\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 11 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator