Step 1 : Find prime factorization of each number.

$$\begin{aligned}11284 =& 2\cdot2\cdot7\cdot13\cdot31\\[8pt]9765 =& 3\cdot3\cdot5\cdot7\cdot31\\[8pt]\end{aligned}$$

(view steps on how to factor 11284 and 9765. )

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

$$\begin{aligned}11284 =& 2\cdot2\cdot\color{blue}{\boxed{7}}\cdot13\cdot\color{red}{\boxed{31}}\\[8pt]9765 =& 3\cdot3\cdot5\cdot\color{blue}{\boxed{7}}\cdot\color{red}{\boxed{31}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 7\cdot31 = 217 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator