The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}16481 =& 16481\\[8pt]16326 =& 2\cdot3\cdot3\cdot907\\[8pt]16473 =& 3\cdot17\cdot17\cdot19\\[8pt]16485 =& 3\cdot5\cdot7\cdot157\\[8pt]16320 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot17\\[8pt]16531 =& 61\cdot271\\[8pt]16269 =& 3\cdot11\cdot17\cdot29\\[8pt]16773 =& 3\cdot5591\\[8pt]\end{aligned}$$(view steps on how to factor 16481, 16326, 16473, 16485, 16320, 16531, 16269 and 16773. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}16481 =& 16481\\[8pt]16326 =& 2\cdot3\cdot3\cdot907\\[8pt]16473 =& 3\cdot17\cdot17\cdot19\\[8pt]16485 =& 3\cdot5\cdot7\cdot157\\[8pt]16320 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3\cdot5\cdot17\\[8pt]16531 =& 61\cdot271\\[8pt]16269 =& 3\cdot11\cdot17\cdot29\\[8pt]16773 =& 3\cdot5591\\[8pt]\end{aligned}$$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} } $.