lwF 122 Bytes
p := (x^2 - 3*x*y + y^2)^4*(3*x - 7*y + 2)^5;
q := (x^2 - 3*x*y + y^2)^3*(3*x - 7*y - 2)^6;
qqq:=gcd(q,p);

factor(qqq);