Find Greatest Common Divisor of 492, 1353 and 615, using prime factorization.

Step 1 : Find prime factorization of each number.

$$\begin{aligned}492 =& 2\cdot2\cdot3\cdot41\\[8pt]1353 =& 3\cdot11\cdot41\\[8pt]615 =& 3\cdot5\cdot41\\[8pt]\end{aligned}$$

(view steps on how to factor 492, 1353 and 615. )

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

$$\begin{aligned}492 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{41}}\\[8pt]1353 =& \color{blue}{\boxed{3}}\cdot11\cdot\color{red}{\boxed{41}}\\[8pt]615 =& \color{blue}{\boxed{3}}\cdot5\cdot\color{red}{\boxed{41}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot41 = 123 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator