When can I divide both sides of an equation if one side is zero

Question

Where K is some positive Integer

For the following examples: $$ K(a+b)(p+q)=0 $$ $$ Ka^2+Kbx+Kc=0 $$

Can I just divide both sides of the equation by K (dividing into 0 on the right) and effectively remove K from the equation?

Update
Assuming K could also be negative but never 0 does this still work?

Answer 1

Yes. It is given that $K$ is always positive, and an integer, so the least value that $K$ can take on is $1$. You just can't divide when $K = 0$.

Answer 2

If $K \neq 0$, multply both sides by $1/K$ gives the results you want.

Answer 3

In your question you are given:$$K(a+b)(p+q)=0$$You should make use of the zero product property to then deduce that either:$$K=0\tag{1}$$$$a+b=0\tag{2}$$$$p+q=0\tag{3}$$You can eliminate (1) as your question states that $K$ is some positive integer.