Example of a set not closed under multiplication

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.

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.

@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.