Find Greatest Common Divisor of 2016 and 927, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}2016 =& 2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\\[8pt]927 =& 3\cdot3\cdot103\\[8pt]\end{aligned}$$

(view steps on how to factor 2016 and 927. )

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

$$\begin{aligned}2016 =& 2\cdot2\cdot2\cdot2\cdot2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot7\\[8pt]927 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot103\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot3 = 9 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator