<s>[INST] A five-digit number $abcde$ is formed by multiplying the number $x$ by $10^{5}$. The unit digit of $x$ determines all the digits of $abcde$. The number $abcde$ has the following properties: it is divisible by $8$, it has no zeros, it is divisible by $3$, and it is divisible by $5$.
The number $x$ has the following properties: it is divisible by $4$, it is a multiple of $6$, it is a multiple of $5$, it is an even number, and it is divisible by $9$.
Which unit digit of $x$ satisfies the conditions for $abcde$ and all the properties of $x$?[/INST]