Find Greatest Common Divisor of 456 and 72, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}456 =& 2\cdot2\cdot2\cdot3\cdot19\\[8pt]72 =& 2\cdot2\cdot2\cdot3\cdot3\\[8pt]\end{aligned}$$

(view steps on how to factor 456 and 72. )

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

$$\begin{aligned}456 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{3}}\cdot19\\[8pt]72 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{2}}\cdot\color{Fuchsia}{\boxed{2}}\cdot\color{Orange}{\boxed{3}}\cdot3\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot2\cdot2\cdot3 = 24 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator