26y^2x^7 = 2 * 13 * y * y * x * x * x * x * x * x * x
52y^3zx^3 = 2 * 2 * 13 * y * y * y * z * x * x * x
169y^2x^5 = 13 * 13 * y * y * x * x * x * x * x
all three parts have 13 * y * y * x * x * x, so the greatest common factor is 13 * y * y * x * x * x = 13 y^2 x^3