Why must a number that is a multiple of a number also be a multiple of the previous multiple's multiple

So, I know the question sounds a bit confusing?
Let me give an example...

8 is a multiple of 4
4 is a multiple of 2
So why must 8 also be a multiple of 2?

I know this is a simple topic and I understand it (don't think I'm an idiot) but is there like a mathematical law that makes this true? If so what is the name of this law? I need the name of this law for a proof I'm writing!

Thanks!

A better example is:

32 is a multiple of 8
8 is a multiple of 2
Therefore 32 is a multiple of 2.

Here is how to justify it:

32 = 4 * 8 = 4 * (4*2) = (4*4) * 2= 16*2

So, what justifies the fact that you observed is the associative law of multiplication.

I guess you can use the Associative Property of multiplication.

Let n be any positive integer.

2n represents a multiple of 2

8n = (2 • 2 • 2) n = 2 (2 • 2 • n) = 2(4n), where 4n also falls the criteria of "positive integer", so

It must be a multiples of 2.

Is is caled transitivity law. Relation of being multiple between natural numbers is a transitive binary relation.