ankitranjan wrote:

Find the remainder of the division (2^69)/9.

A. 1

B. 4

C. 5

D. 8

E. 7

Let’s find a remainder pattern:

2^1/9 has a remainder of 2

2^2/9 has a remainder of 4

2^3/9 has a remainder of 8

2^4/9 = 16/9 has a remainder of 7

2^5/9 = 32/9 has a remainder of 5

2^6/9 = 64/9 has remainder of 1

2^7/9 = 128/9 has a remainder of 2

We see the pattern of remainders is 2-4-8-7-5-1, so it repeats every 6 exponents.

Thus, 2^66/9 has a remainder of 1, 2^67/9 has a remainder of 2, 2^68/9 has a remainder of 4, and 2^69/9 has a remainder of 8.

Answer: D

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