The GCD of given numbers is 35.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}4655 =& 5\cdot7\cdot7\cdot19\\[8pt]12075 =& 3\cdot5\cdot5\cdot7\cdot23\\[8pt]\end{aligned}$$(view steps on how to factor 4655 and 12075. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}4655 =& \color{blue}{\boxed{5}}\cdot\color{red}{\boxed{7}}\cdot7\cdot19\\[8pt]12075 =& 3\cdot\color{blue}{\boxed{5}}\cdot5\cdot\color{red}{\boxed{7}}\cdot23\\[8pt]\end{aligned}$$Step 3 : Multiply the boxed numbers together:
$$ GCD = 5\cdot7 = 35 $$This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.