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how to find out remander when 3^2009 is divided by 21 ???????????????

how to find out remander when 3^2009 is divided by 21 ??????????????? 

Grade:10

1 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-9.4}$Here we calculate remainder when $3^{2008}$ is divided by $7$.\\\\ So remainder when $3(3^{3})^{669}$ is divided by $7$\\\\So $3^3=(-1)\mod(7)$. So $(3^3)^{669}=(-1)\mod (7)$\\\\So $3(3^{3})^{669}=-3\mod(7) = 4 \mod(7)$\\\\So Remainder is $=4$\\\\So remainder when $3^{2009}$ is divided by $21$ is equal to $=12.$

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