Find Greatest Common Divisor of 30, 60 and 90, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}30 =& 2\cdot3\cdot5\\[8pt]60 =& 2\cdot2\cdot3\cdot5\\[8pt]90 =& 2\cdot3\cdot3\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 30, 60 and 90. )

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

$$\begin{aligned}30 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{5}}\\[8pt]60 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{5}}\\[8pt]90 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot3\cdot\color{Fuchsia}{\boxed{5}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot5 = 30 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator