Find Greatest Common Divisor of 6, 42, 12, 52 and 20, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}6 =& 2\cdot3\\[8pt]42 =& 2\cdot3\cdot7\\[8pt]12 =& 2\cdot2\cdot3\\[8pt]52 =& 2\cdot2\cdot13\\[8pt]20 =& 2\cdot2\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 6, 42, 12, 52 and 20. )

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

$$\begin{aligned}6 =& \color{blue}{\boxed{2}}\cdot3\\[8pt]42 =& \color{blue}{\boxed{2}}\cdot3\cdot7\\[8pt]12 =& \color{blue}{\boxed{2}}\cdot2\cdot3\\[8pt]52 =& \color{blue}{\boxed{2}}\cdot2\cdot13\\[8pt]20 =& \color{blue}{\boxed{2}}\cdot2\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2 $$

GCD Calculator