The GCF of 4, 6, 9, and 8 is 1 because 4 is 2 * 2 and 9 is 3 * 3, so 1 is the only thing that will go into 4, 6, 9, and 8 evenly.
0 is weird. From this page ( http://math.info/Arithmetic/GCF/ ), "GCF(a, 0) = |a|, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is |a|."
But since the GCF of 4, 6, 9, 8 is 1, the GCF of 4, 6, 9, 0, 8 is still just 1.