The GCD of given numbers is 8925.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}8925 =& 3\cdot5\cdot5\cdot7\cdot17\\[8pt]76576500 =& 2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot5\cdot7\cdot11\cdot13\cdot17\\[8pt]\end{aligned}$$(view steps on how to factor 8925 and 76576500. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}8925 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{5}}\cdot\color{Orange}{\boxed{7}}\cdot\color{Purple}{\boxed{17}}\\[8pt]76576500 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot3\cdot\color{red}{\boxed{5}}\cdot\color{Fuchsia}{\boxed{5}}\cdot5\cdot\color{Orange}{\boxed{7}}\cdot11\cdot13\cdot\color{Purple}{\boxed{17}}\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 3\cdot5\cdot5\cdot7\cdot17 = 8925 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.