Step 1 : Find prime factorization of each number.

$$\begin{aligned}1625 =& 5\cdot5\cdot5\cdot13\\[8pt]975 =& 3\cdot5\cdot5\cdot13\\[8pt]\end{aligned}$$

(view steps on how to factor 1625 and 975. )

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

$$\begin{aligned}1625 =& \color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\cdot5\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]975 =& 3\cdot\color{blue}{\boxed{5}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{13}}\\[8pt]\end{aligned}$$

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