Question

Find the remainder when ${286}^{143}$ is divided by 20?

• A. 16
• B. 56
• C. 6
• D. None of these

Answer 1

The correct option is A 16

${286}^{143}=({143}^4{)}^{35}\times ({143}^3)\times (2^{143})$
This can be re-written as $({43}^4{)}^{35}\times ({43}^3)\times (2^{10}{)}^{14}\times \left(2^3\right)$ since we are concerned only with the last two digits.
Now, $({43}^4{)}^{35}\times ({43}^3)\times (2^{10}{)}^{14}\times \left(2^3\right)=(49\times 49{)}^{35}\times (49\times 43)\times 76\times 08=(01{)}^{35}\times \left(07\right)\times 08=01\times 56=56$
Finally, when 56 is divided by 20, it will leave a remainder of 16.