Hey, could I get receive some help with these problems, thanks.

1) Show that p is a prime number and p divides the product ab then a divides a or b divides b.

2) Let Tn be the highest power of 2 that divides n. Show that Tnm = Tn + Tm

3) Let n, c, and d be three integers. Show that if d * c divides n * c then d divides n.