Find Greatest Common Divisor of 48, 72, 108, 120, 144, 180, 192, 216, 240 and 300, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}48 =& 2\cdot2\cdot2\cdot2\cdot3\\[8pt]72 =& 2\cdot2\cdot2\cdot3\cdot3\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]120 =& 2\cdot2\cdot2\cdot3\cdot5\\[8pt]144 =& 2\cdot2\cdot2\cdot2\cdot3\cdot3\\[8pt]180 =& 2\cdot2\cdot3\cdot3\cdot5\\[8pt]192 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\\[8pt]216 =& 2\cdot2\cdot2\cdot3\cdot3\cdot3\\[8pt]240 =& 2\cdot2\cdot2\cdot2\cdot3\cdot5\\[8pt]300 =& 2\cdot2\cdot3\cdot5\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 48, 72, 108, 120, 144, 180, 192, 216, 240 and 300. )

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

$$\begin{aligned}48 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot\color{Fuchsia}{\boxed{3}}\\[8pt]72 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot3\\[8pt]108 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot3\\[8pt]120 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot5\\[8pt]144 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot3\\[8pt]180 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot5\\[8pt]192 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot\color{Fuchsia}{\boxed{3}}\\[8pt]216 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot3\\[8pt]240 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot2\cdot2\cdot\color{Fuchsia}{\boxed{3}}\cdot5\\[8pt]300 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{3}}\cdot5\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot3 = 12 $$

GCD Calculator