Find Greatest Common Divisor of 255, 165 and 195, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}255 =& 3\cdot5\cdot17\\[8pt]165 =& 3\cdot5\cdot11\\[8pt]195 =& 3\cdot5\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 255, 165 and 195. )

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

$$\begin{aligned}255 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot17\\[8pt]165 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot11\\[8pt]195 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot13\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot5 = 15 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator