Step 1 : Find prime factorization of each number.

$$\begin{aligned}13860 =& 2\cdot2\cdot3\cdot3\cdot5\cdot7\cdot11\\[8pt]727650 =& 2\cdot3\cdot3\cdot3\cdot5\cdot5\cdot7\cdot7\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 13860 and 727650. )

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

$$\begin{aligned}13860 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot\color{Orange}{\boxed{5}}\cdot\color{Purple}{\boxed{7}}\cdot\color{blue}{\boxed{11}}\\[8pt]727650 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{3}}\cdot3\cdot\color{Orange}{\boxed{5}}\cdot5\cdot\color{Purple}{\boxed{7}}\cdot7\cdot\color{blue}{\boxed{11}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot3\cdot5\cdot7\cdot11 = 6930 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator