All multiples are composite numbers.
Zero is not a composite number, therefore it cannot be a multiple.
0 and 1 have special roles in arithmetic. 0 is the identity element in addition, 1 is the identity element in multiplication.
In multiplication, 0 has its own special property that is derived from the distributive law:
a.(b-b)=a.b - a.b
a.0 = 0
for all a.
Note this is not a one-to-one mapping, therefore there is no inverse and div by 0 is undefined.
Youre right but we should also take it into consideration that when counting the multiples of 3, the first number to be considered is zero because is it also a real number and an addition 3 makes us get the second multiple of 3.