Find Greatest Common Divisor of 84, 36 and 75, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}84 =& 2\cdot2\cdot3\cdot7\\[8pt]36 =& 2\cdot2\cdot3\cdot3\\[8pt]75 =& 3\cdot5\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 84, 36 and 75. )

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

$$\begin{aligned}84 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot7\\[8pt]36 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot3\\[8pt]75 =& \color{blue}{\boxed{3}}\cdot5\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator