Examples
6 is divisible by 3 because 6=3x2
14 is divisible by 7 because 14=7x2
Counterexamples
8 is not divisible by 7
13 is not divisible by 5
We denote b|a if a is divisible by b. We can also say that a is a multiple of b.
If b|a and c|b, then c|a
Proof: Because b|a, there exists some arbitrary integer x such that a=xb.
Similarly, since c|b is true, there exists some aribitrary integer y such that b=xc.
From this, we know that a=xyc. Since x, y is an integer, therefore xy is an integer. Therefore, from the definition of divisibility, a is divisible by c and equivilantly c|a
If m|a and m|a, then m|(ax+by) with x, y being integers
If mn|a then m|a and n|a