Find Greatest Common Divisor of 36, 87, 90 and 120, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}36 =& 2\cdot2\cdot3\cdot3\\[8pt]87 =& 3\cdot29\\[8pt]90 =& 2\cdot3\cdot3\cdot5\\[8pt]120 =& 2\cdot2\cdot2\cdot3\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 36, 87, 90 and 120. )

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

$$\begin{aligned}36 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot3\\[8pt]87 =& \color{blue}{\boxed{3}}\cdot29\\[8pt]90 =& 2\cdot\color{blue}{\boxed{3}}\cdot3\cdot5\\[8pt]120 =& 2\cdot2\cdot2\cdot\color{blue}{\boxed{3}}\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3 $$

GCD Calculator