Find Greatest Common Divisor of 32 and 16, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}32 =& 2\cdot2\cdot2\cdot2\cdot2\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]\end{aligned}$$

(view steps on how to factor 32 and 16. )

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

$$\begin{aligned}32 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\cdot2\\[8pt]16 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{2}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot2 = 16 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator