The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}7 =& 7\\[8pt]17 =& 17\\[8pt]11 =& 11\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]13 =& 13\\[8pt]347 =& 347\\[8pt]19 =& 19\\[8pt]11 =& 11\\[8pt]33 =& 3\cdot11\\[8pt]13 =& 13\\[8pt]30 =& 2\cdot3\cdot5\\[8pt]\end{aligned}$$(view steps on how to factor 7, 17, 11, 28, 13, 347, 19, 11, 33, 13 and 30. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}7 =& 7\\[8pt]17 =& 17\\[8pt]11 =& 11\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]13 =& 13\\[8pt]347 =& 347\\[8pt]19 =& 19\\[8pt]11 =& 11\\[8pt]33 =& 3\cdot11\\[8pt]13 =& 13\\[8pt]30 =& 2\cdot3\cdot5\\[8pt]\end{aligned}$$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} } $.