Question

The last digit of the number $7^{886}$is

• A. $9$
• B. $7$
• C. $3$
• D. $1$

Answer 1

The correct option is A

$9$

Explanation for the correct option

The last digit in $7^1$ is $7$

The last digit in $7^2$ is $9$

Similarly for $7^3$ is $3$

for $7^4$ it is $1$ and for $7^5$ it is $7$ again.

Therefore for base $7$ the cyclicity is $4$

Now, the relation between the last digit and the number as a multiple of $4$ is:

$$\begin{gathered} 4n=1 \\ \Rightarrow 4n+1=7 \\ \Rightarrow 4n+2=9 \\ \Rightarrow 4n+3=3 \\ \therefore 886=884+2 \end{gathered}$$

i.e.$4n+2$

So the last digit will be $9$.

Hence correct option (A)