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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