I couldn't prove the question below, can someone help me on this? Please do not refer to other answers, thank you!

Let a, b, c be positive integers and b, c be coprime integers. Prove that hof(a, bc) | c . hof(a, b) and hof(a, bc) | b . hof(a, c). . hof(a, bc) | hof(a, b) . hof(a, c). Hint: hof(ac, bc) = c . hof(a, b) for any positive integers a, b, c.)