Question

What is the last digit of ${518}^{163}+{142}^{157}$?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

It is a general observation that unit digit of a number repeats after fourth power for all number.

unit digit of ${518}^{163}$ so we divide $163$ by $4$ and find remainder i.e- $3$

now it comes for unit digit $8^3$=unit digit(2)

unit digit of ${142}^{157}$ so we divide $157$ by $4$ and find remainder i.e- $1$

now it comes for unit digit $2^1$=unit digit(2)

hence the sum of unit digit is $2+2=4$