Find Greatest Common Divisor of 78, 117 and 351, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}78 =& 2\cdot3\cdot13\\[8pt]117 =& 3\cdot3\cdot13\\[8pt]351 =& 3\cdot3\cdot3\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 78, 117 and 351. )

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

$$\begin{aligned}78 =& 2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{13}}\\[8pt]117 =& \color{blue}{\boxed{3}}\cdot3\cdot\color{red}{\boxed{13}}\\[8pt]351 =& \color{blue}{\boxed{3}}\cdot3\cdot3\cdot\color{red}{\boxed{13}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot13 = 39 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator