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UPSC Prelims

Mathematics

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Elementary Algebra / प्रारंभिक बीजगणित

Q5 2021, Elementary Algebra

If 3²⁰¹⁹ is divided by 10, then what is the remainder?

यदि 3 ^ 2019 को 10 से विभाजित किया जाए, तो शेष क्या होगा?

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Since, unit place of the power of 3 repeats after every 4 steps (i.e., it has a cyclicity of 4).

Now, dividing 2019 by 4 we get a remainder of 3.

Hence, 3^2019 will have the same last digit as that of 33, i.e., 7.

(3^3)/10 = 27/10 Hence, the remainder will be 7.

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