The GCD of given numbers is 1.
Step 1 : Find prime factorization of each number.
$$\begin{aligned}121 =& 11\cdot11\\[8pt]645 =& 3\cdot5\cdot43\\[8pt]100 =& 2\cdot2\cdot5\cdot5\\[8pt]408 =& 2\cdot2\cdot2\cdot3\cdot17\\[8pt]832 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot13\\[8pt]19 =& 19\\[8pt]2 =& 2\\[8pt]432 =& 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\\[8pt]902 =& 2\cdot11\cdot41\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]176 =& 2\cdot2\cdot2\cdot2\cdot11\\[8pt]640 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]19 =& 19\\[8pt]\end{aligned}$$(view steps on how to factor 121, 645, 100, 408, 832, 19, 2, 432, 902, 8, 176, 640 and 19. )
Step 2 : Put a box around factors that are common for all numbers:
$$\begin{aligned}121 =& 11\cdot11\\[8pt]645 =& 3\cdot5\cdot43\\[8pt]100 =& 2\cdot2\cdot5\cdot5\\[8pt]408 =& 2\cdot2\cdot2\cdot3\cdot17\\[8pt]832 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot13\\[8pt]19 =& 19\\[8pt]2 =& 2\\[8pt]432 =& 2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot3\\[8pt]902 =& 2\cdot11\cdot41\\[8pt]8 =& 2\cdot2\cdot2\\[8pt]176 =& 2\cdot2\cdot2\cdot2\cdot11\\[8pt]640 =& 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\\[8pt]19 =& 19\\[8pt]\end{aligned}$$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} } $.