Show that if ac divides bc then a divides bSolutionLet a b c

Show that if ac divides bc, then a divides b.

Solution

Let a, b, c be integers.

Given ac divides bc.

Then

bc = ac * k for some integer k.

Then (bc) / c = (ac * k) / c

So b = a * k

Since k is an integer, a divides b