Question : What is the remainder when $3^8$ is divided by 7?
Option 1: 5
Option 2: 4
Option 3: 6
Option 4: 2
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Correct Answer: 2
Solution : To find: The remainder when $3^8$ is divided by 7 = remainder ($\frac{3^8}{7}$) = remainder ($\frac{(3^2)^4}{7}$) = remainder ($\frac{(9)^4}{7}$) 9 divided by 7 will leave the remainder of 2. So, remainder = remainder ($\frac{2^4}{7})$ = remainder ($\frac{16}{7}$) = 2 Hence, the correct answer is 2.
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