Step 1 : Find prime factorization of each number.

$$\begin{aligned}650 =& 2\cdot5\cdot5\cdot13\\[8pt]325 =& 5\cdot5\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 650 and 325. )

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

$$\begin{aligned}650 =& 2\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]325 =& \color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 5\cdot5\cdot13 = 325 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator