Find Greatest Common Divisor of 36, 48, 84 and 140, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}36 =& 2\cdot2\cdot3\cdot3\\[8pt]48 =& 2\cdot2\cdot2\cdot2\cdot3\\[8pt]84 =& 2\cdot2\cdot3\cdot7\\[8pt]140 =& 2\cdot2\cdot5\cdot7\\[8pt]\end{aligned}$$

(view steps on how to factor 36, 48, 84 and 140. )

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

$$\begin{aligned}36 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot3\cdot3\\[8pt]48 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot3\\[8pt]84 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot3\cdot7\\[8pt]140 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot5\cdot7\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2 = 4 $$

GCD Calculator