The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}19 =& 19\\[8pt]29 =& 29\\[8pt]35 =& 5\cdot7\\[8pt]36 =& 2\cdot2\cdot3\cdot3\\[8pt]44 =& 2\cdot2\cdot11\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]\end{aligned}$$(view steps on how to factor 19, 29, 35, 36, 44 and 16. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}19 =& 19\\[8pt]29 =& 29\\[8pt]35 =& 5\cdot7\\[8pt]36 =& 2\cdot2\cdot3\cdot3\\[8pt]44 =& 2\cdot2\cdot11\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]\end{aligned}$$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} } $.