Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$ As the title says, if a number is divisible by a number, is it always divisible by that number's factors?
An example being that $100$ is divisible by $20$, it is also divisible by $10, 5, 4, 2$ as well?
Does this always apply?

Write $a$ as a product of primes. We have:
$$\mu k = b \tag 1$$
where $\mu$ is either a prime factor of $a$ or a product of some of its prime factors, $k$ is the product of the rest of the factors. Now, $(1)$ is the notation of divisibility read as $\mu$ divides $b$.
