Find Greatest Common Divisor of 576, 1152, 1280, 136 and 200, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}576 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\\[8pt]1152 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\\[8pt]1280 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]136 =& 2\cdot2\cdot2\cdot17\\[8pt]200 =& 2\cdot2\cdot2\cdot5\cdot5\\[8pt]\end{aligned}$$

(view steps on how to factor 576, 1152, 1280, 136 and 200. )

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

$$\begin{aligned}576 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot2\cdot2\cdot3\cdot3\\[8pt]1152 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\\[8pt]1280 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]136 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot17\\[8pt]200 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot5\cdot5\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2 = 8 $$

GCD Calculator