Find Greatest Common Divisor of 33728 and 26880, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}33728 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot17\cdot31\\[8pt]26880 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot7\\[8pt]\end{aligned}$$

(view steps on how to factor 33728 and 26880. )

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

$$\begin{aligned}33728 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot\color{blue}{\boxed{2}}\cdot17\cdot31\\[8pt]26880 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot\color{Purple}{\boxed{2}}\cdot\color{blue}{\boxed{2}}\cdot2\cdot2\cdot3\cdot5\cdot7\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2\cdot2\cdot2 = 64 $$

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator