Step 1 : Find prime factorization of each number.

$$\begin{aligned}81 =& 3\cdot3\cdot3\cdot3\\[8pt]729 =& 3\cdot3\cdot3\cdot3\cdot3\cdot3\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]153 =& 3\cdot3\cdot17\\[8pt]198 =& 2\cdot3\cdot3\cdot11\\[8pt]\end{aligned}$$

(view steps on how to factor 81, 729, 108, 153 and 198. )

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

$$\begin{aligned}81 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot3\cdot3\\[8pt]729 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot3\cdot3\cdot3\cdot3\\[8pt]108 =& 2\cdot2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot3\\[8pt]153 =& \color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot17\\[8pt]198 =& 2\cdot\color{blue}{\boxed{3}}\cdot\color{red}{\boxed{3}}\cdot11\\[8pt]\end{aligned}$$

Step 3 : Multiply the boxed numbers together:

$$ GCD = 3\cdot3 = 9 $$

GCD Calculator