Step 1 : Find prime factorization of each number.

$$\begin{aligned}5655 =& 3\cdot5\cdot13\cdot29\\[8pt]12075 =& 3\cdot5\cdot5\cdot7\cdot23\\[8pt]\end{aligned}$$

(view steps on how to factor 5655 and 12075. )

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

$$\begin{aligned}5655 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot13\cdot29\\[8pt]12075 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{5}}\cdot5\cdot7\cdot23\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot5 = 15 $$

This solution can be visualized using a Venn diagram.

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

GCD Calculator