(i) Let a, b, and c be integers with gcf(a,b) = gcf(a,c) = 1. Show that gcf(a,bc) = 1.

There's a more general case to this in (ii) of the same problem, where if [tex]{a_i}[/tex] is relatively prime with b for then the product of [tex]{a_i}[/tex] is relatively prime with b.

If you could give me a hint on how to prove (i), that would be greatly appreciated.