Primitive Recursive Function for Division and Hailstone function Are division and Hailstone primitive recursion function?

$$\text{Div}(x,y) = \begin{cases}
x/y,  &amp; \text{if $y$ divides $x$ } \\
0, &amp; \text{otherwise}
\end{cases}$$ 

$$\text{Hailstone}(n) =\begin{cases}
3n + 1,  &amp; \text{if $n$ is odd } \\
n/2, &amp; \text{if $n$ is even}
\end{cases}$$ 

I tried to solve division in this way
$$\text{Div}(0,y) = 0 $$
$$\text{Div}(x+y,y) = \text{Div}(x,y) + 1$$

I do not know how to proceed from here. Can anyone help me?
For your division example, what would the case be if y was equal to zero?  

The function is undefined if y = 0.  Thus, it is not a total function.  Thus, division is not primitively recursive, as all primitively recursive functions are total functions.