Question

Find the remainder when ${{7^{27}}^{16}}^3$ is divided by 10.

• A. 7
• B. 9
• C. 1
• D. 3

Answer 1

Answer: (A)

7

We need to find out the unit digit of the given number.

$\frac{{{27}^{16}}^3}{4}=\frac{{27}^{evennumber}}{4}=\frac{(-1{)}^{evennumber}}{4}=1$

Now the question changes to finding the unit digit of $7^{4n+1}$. From the power cycle of 7, unit digit will be 7. Hence, the remainder is 7.