Find Greatest Common Divisor of 64, 224, 96 and 608, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}64 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\\[8pt]224 =& 2\cdot2\cdot2\cdot2\cdot2\cdot7\\[8pt]96 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\\[8pt]608 =& 2\cdot2\cdot2\cdot2\cdot2\cdot19\\[8pt]\end{aligned}$$

(view steps on how to factor 64, 224, 96 and 608. )

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

$$\begin{aligned}64 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot2\\[8pt]224 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot7\\[8pt]96 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot3\\[8pt]608 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot19\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2 = 32 $$

GCD Calculator