The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}35 =& 5\cdot7\\[8pt]88 =& 2\cdot2\cdot2\cdot11\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]260 =& 2\cdot2\cdot5\cdot13\\[8pt]92 =& 2\cdot2\cdot23\\[8pt]140 =& 2\cdot2\cdot5\cdot7\\[8pt]100 =& 2\cdot2\cdot5\cdot5\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]344 =& 2\cdot2\cdot2\cdot43\\[8pt]\end{aligned}$$(view steps on how to factor 35, 88, 16, 260, 92, 140, 100, 80, 80 and 344. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}35 =& 5\cdot7\\[8pt]88 =& 2\cdot2\cdot2\cdot11\\[8pt]16 =& 2\cdot2\cdot2\cdot2\\[8pt]260 =& 2\cdot2\cdot5\cdot13\\[8pt]92 =& 2\cdot2\cdot23\\[8pt]140 =& 2\cdot2\cdot5\cdot7\\[8pt]100 =& 2\cdot2\cdot5\cdot5\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]80 =& 2\cdot2\cdot2\cdot2\cdot5\\[8pt]344 =& 2\cdot2\cdot2\cdot43\\[8pt]\end{aligned}$$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} } $.