Step 1 : Find prime factorization of each number.

$$\begin{aligned}30 =& 2\cdot3\cdot5\\[8pt]33 =& 3\cdot11\\[8pt]42 =& 2\cdot3\cdot7\\[8pt]45 =& 3\cdot3\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 30, 33, 42 and 45. )

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

$$\begin{aligned}30 =& 2\cdot\color{blue}{\boxed{3}}\cdot5\\[8pt]33 =& \color{blue}{\boxed{3}}\cdot11\\[8pt]42 =& 2\cdot\color{blue}{\boxed{3}}\cdot7\\[8pt]45 =& \color{blue}{\boxed{3}}\cdot3\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3 $$

GCD Calculator