Are division and Hailstone primitive recursion function?
$$\text{Div}(x,y) = \begin{cases}
x/y, & \text{if $y$ divides $x$ } \\
0, & \text{otherwise}
\end{cases}$$
$$\text{Hailstone}(n) =\begin{cases}
3n + 1, & \text{if $n$ is odd } \\
n/2, & \text{if $n$ is even}
\end{cases}$$
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?