Step 1 : Find prime factorization of each number.

$$\begin{aligned}210 =& 2\cdot3\cdot5\cdot7\\[8pt]355 =& 5\cdot71\\[8pt]690 =& 2\cdot3\cdot5\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 210, 355 and 690. )

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

$$\begin{aligned}210 =& 2\cdot3\cdot\color{blue}{\boxed{5}}\cdot7\\[8pt]355 =& \color{blue}{\boxed{5}}\cdot71\\[8pt]690 =& 2\cdot3\cdot\color{blue}{\boxed{5}}\cdot23\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 5 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator