Find Greatest Common Divisor of 16146 and 299, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}16146 =& 2\cdot3\cdot3\cdot3\cdot13\cdot23\\[8pt]299 =& 13\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 16146 and 299. )

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

$$\begin{aligned}16146 =& 2\cdot3\cdot3\cdot3\cdot\color{blue}{\boxed{13}}\cdot\color{red}{\boxed{23}}\\[8pt]299 =& \color{blue}{\boxed{13}}\cdot\color{red}{\boxed{23}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 13\cdot23 = 299 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator