lwG 234 Bytes
p := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^4*(3*x-7*y+2*z-3)^5;
q := (7*y*x^2*z^2-3*x*y*z+11*(x+1)*y^2+5*z+1)^3*(3*x-7*y+2*z+3)^6;
qqq:= gcd(p, q);
factor(qqq);
p:=normal(p % 181);
q:=normal(q % 181);
qqq:= gcd(p, q);
factor(qqq);