Example of a set not closed under multiplication

Question

It might be a stupid question, but can you give me some example of multiplication not being closed in some set?

I could find a case in "addition"(e.g., a set of odd numbers is not closed under addition) but am struggling to find an example for multiplication.

Answer 1

Consider the set of negative integers, this set has the property that if you multiply any two negative integers you will never get another negative integer.

Answer 2

@Rowing0914 gave a nice example where multiplication acts to produce a different type of object.

Consider the set of all prime numbers $p_i$. By definition, none of these share any common factors.