Quantitative Aptitude Ques 606

Question: The greatest common divisor of $ {3^{3^{333}}}+1 $ and $ {3^{3^{334}}}+1 $ is

Options:

A) $ {3^{3^{333}}}+1 $

B) 20

C) 2

D) 1

Show Answer

Answer:

Correct Answer: D

Solution:

  • Given, $ {3^{3^{333}}}+1 $ and $ {3^{3^{334}}}+1=27^{333}+1 $ and $ 27^{334}+1 $ Now $ (x^{m}+a^{m}) $ is divisible by $ (x+a) $ for odd m.

$ \therefore $ $ (27+1) $ divides $ (27^{333}+1) $ and does not divide $ (27^{334}+1). $

$ \therefore $ HCF of $ (27^{333}+1) $ and $ (27^{334}+1) $ is 1.

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