Find Greatest Common Divisor of 42, 78 and 96, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}42 =& 2\cdot3\cdot7\\[8pt]78 =& 2\cdot3\cdot13\\[8pt]96 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\\[8pt]\end{aligned}$$

(view steps on how to factor 42, 78 and 96. )

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

$$\begin{aligned}42 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot7\\[8pt]78 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot13\\[8pt]96 =& \color{blue}{\boxed{2}}\cdot2\cdot2\cdot2\cdot2\cdot\color{red}{\boxed{3}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3 = 6 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator