The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}169 =& 13\cdot13\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]160 =& 2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]292 =& 2\cdot2\cdot73\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]56 =& 2\cdot2\cdot2\cdot7\\[8pt]68 =& 2\cdot2\cdot17\\[8pt]72 =& 2\cdot2\cdot2\cdot3\cdot3\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]124 =& 2\cdot2\cdot31\\[8pt]52 =& 2\cdot2\cdot13\\[8pt]264 =& 2\cdot2\cdot2\cdot3\cdot11\\[8pt]\end{aligned}$$(view steps on how to factor 169, 28, 16, 8, 160, 28, 292, 108, 56, 68, 72, 28, 124, 52 and 264. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}169 =& 13\cdot13\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]160 =& 2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]292 =& 2\cdot2\cdot73\\[8pt]108 =& 2\cdot2\cdot3\cdot3\cdot3\\[8pt]56 =& 2\cdot2\cdot2\cdot7\\[8pt]68 =& 2\cdot2\cdot17\\[8pt]72 =& 2\cdot2\cdot2\cdot3\cdot3\\[8pt]28 =& 2\cdot2\cdot7\\[8pt]124 =& 2\cdot2\cdot31\\[8pt]52 =& 2\cdot2\cdot13\\[8pt]264 =& 2\cdot2\cdot2\cdot3\cdot11\\[8pt]\end{aligned}$$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} } $.