Question

If unit's digit of $7^3$ is $3$ then what will be the unit's digit of $7^{11}$.

• A. $7$
• B. $9$
• C. $3$
• D. $1$

Answer 1

Answer: (C)

$3$

$7^{11}=7^3\times 7^3\times 7^3\times 7^2$

$\text{unit digit of}{7}^{11}=\text{unit digit of}{7}^3\times \text{unit digit of}{7}^3\times \text{unit digit of}{7}^3\times \text{unit digit of}{7}^2$

Given that unit digit of $7^3$ is 3.

$\therefore$ taking unit digits-

$\text{unit digit of}{7}^{11}=3\times 3\times 3\times \text{unit digit of}{7}^2=3\times 3\times 3\times \text{unit digit of}49$

$\Rightarrow \text{unit digit of}{7}^{11}=\text{unit digit of}27\times \text{unit digit of}49=3\left(\text{unit digit}\right)$

Hence, the correct answer is 3.