Step 1 : Find prime factorization of each number.

$$\begin{aligned}81 =& 3\cdot3\cdot3\cdot3\\[8pt]729 =& 3\cdot3\cdot3\cdot3\cdot3\cdot3\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]153 =& 3\cdot3\cdot17\\[8pt]193 =& 193\\[8pt]\end{aligned}$$

(view steps on how to factor 81, 729, 108, 153 and 193. )

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

$$\begin{aligned}81 =& 3\cdot3\cdot3\cdot3\\[8pt]729 =& 3\cdot3\cdot3\cdot3\cdot3\cdot3\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]153 =& 3\cdot3\cdot17\\[8pt]193 =& 193\\[8pt]\end{aligned}$$

Note that in this example numbers do not have any common factors.

Step 3 : Multiply the boxed numbers together:

Since there is no boxed numbers we conclude that $~\color{blue}{ \text{GCD = 1} } $.

GCD Calculator