Question

Remainder when 6^50 is divided by 215?

Answer 1

hope it helps you....

Answer 2

$6^{50} \div 215 = 6^{3(20) + 2} \div 215$

$6^{50} \div 215 = [ (6^3)^{20} \times 6^2}]\div 215$

$6^{50} \div 215 = [ (216)^{20} \times 6^2}]\div 215$

$6^{50} \div 215 =(216 \div 215 )^{20} \times (36 \div 215)}$

Find the reminder:

$\text {Remainder of } (216\div 215 )^{20} = (1)^{20} = 1$

$\text {Remainder of } (36 \div 215 ) = 36$

$6^{50} \div 215 = \text {Remainder : } 1 \times 36 = 36$

Answer: The remainder is 36