Answer:
This isn't true.
Step-by-step explanation:
Think of the case a=2, b=3 and c=6. We have that a|b, since 2|6.
We also have that ab=c, since 2*3=6. However, it is NOT true that a|b, as 2 does NOT divide 3. As this you can construct many other examples where a|c and ab=c BUT a does NOT divide b.
Other counterexamples:
a=2, b=5, c=10
a=2, b=7, c=14
a=2, b=11, c=22
a=2, b=13, c=26
