Find Greatest Common Divisor of 102, 170 and 255, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}102 =& 2\cdot3\cdot17\\[8pt]170 =& 2\cdot5\cdot17\\[8pt]255 =& 3\cdot5\cdot17\\[8pt]\end{aligned}$$

(view steps on how to factor 102, 170 and 255. )

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

$$\begin{aligned}102 =& 2\cdot3\cdot\color{blue}{\boxed{17}}\\[8pt]170 =& 2\cdot5\cdot\color{blue}{\boxed{17}}\\[8pt]255 =& 3\cdot5\cdot\color{blue}{\boxed{17}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 17 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator