Order of an element

Computation.
- $\bar 0$: order $1$.
- $\bar 1$: $8\cdot1\equiv0$, order $8$.
- $\bar 2$: $4\cdot2=8\equiv0$, order $4$.
- $\bar 3$: $8\cdot3=24\equiv0$, order $8$.
- $\bar 4$: $2\cdot4=8\equiv0$, order $2$.
- $\bar 5$: $8\cdot5=40\equiv0$, order $8$.
- $\bar 6$: $4\cdot6=24\equiv0$, order $4$.
- $\bar 7$: $8\cdot7=56\equiv0$, order $8$.

Conclusion. Orders: $1,8,4,8,2,8,4,8$.

Remark. The order of $\bar k$ in $\mathbb{Z}/n\mathbb{Z}$ is $n/\gcd(k,n)$.