tis always a good idea when factoring to start off with a quick prime factoring.
[tex]\begin{array}{llll} 52&=&2\cdot 2\cdot 13\\\\ 77&=&\boxed{7}\cdot 11\\\\ 91&=&\boxed{7}\cdot 13\\\\ 124&=&2\cdot 2\cdot 31\\\\ 217&=&\boxed{7}\cdot 31 \end{array}[/tex]
