Question:
The remainder when $2^{2016}$ is divided by $63$, is
The remainder when $2^{2016}$ is divided by $63$, is
Updated On: Aug 2, 2024
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The Correct Option is A
Solution and Explanation
\(2^{2016}=\left(2^{6}\right)^{336}=(64)^{336}=(63+1)^{336}\)
\((63+1)^{336}=^{366}C_0(63)^0(1)^{366}+^{366}C_1(63)^1(1)^{364}+^{366}C_2(63)^2(1)^{362}+…… = 1+63K\)
\(\therefore\) Remainder \(=1\)
So, the correct option is (A): \(1\)
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The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
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