Step 1 : Find prime factorization of each number.

$$\begin{aligned}5844 =& 2\cdot2\cdot3\cdot487\\[8pt]8766 =& 2\cdot3\cdot3\cdot487\\[8pt]\end{aligned}$$

(view steps on how to factor 5844 and 8766. )

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

$$\begin{aligned}5844 =& \color{blue}{\boxed{2}}\cdot2\cdot\color{red}{\boxed{3}}\cdot\color{Fuchsia}{\boxed{487}}\\[8pt]8766 =& \color{blue}{\boxed{2}}\cdot\color{red}{\boxed{3}}\cdot3\cdot\color{Fuchsia}{\boxed{487}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 2\cdot3\cdot487 = 2922 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator