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Find the remainder when 67¹⁰⁷ is divided by 7.

14
22
31
46

Answer:- 1

Explanation:-

Solution:

\begin{aligned} \frac{67^{107}}{7} \\ O r, \frac{{(7 \times 9 + 4)}^{107}}{7} \\ The remainder will be same as \\ \frac{4^{107}}{7} \\ O r, \frac{4^{3}}{7} \\ O r, \frac{64}{7} \\ Required Remainder = 1 \end{aligned}

$\eqalign{ & \frac{{{{67}^{107}}}}{7} \cr & Or,\,\frac{{{{\left( {7 \times 9 + 4} \right)}^{107}}}}{7} \cr & {\text{The}}\,{\text{remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}} \cr & \frac{{{4^{107}}}}{7} \cr & Or,\,\frac{{{4^3}}}{7} \cr & Or,\,\frac{{64}}{7} \cr & {\text{Required}}\,{\text{Remainder}} = 1 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} \frac{67^{107}}{7} \\ O r, \frac{{(7 \times 9 + 4)}^{107}}{7} \\ The remainder will be same as \\ \frac{4^{107}}{7} \\ O r, \frac{4^{3}}{7} \\ O r, \frac{64}{7} \\ Required Remainder = 1 \end{aligned}

$\eqalign{ & \frac{{{{67}^{107}}}}{7} \cr & Or,\,\frac{{{{\left( {7 \times 9 + 4} \right)}^{107}}}}{7} \cr & {\text{The}}\,{\text{remainder}}\,{\text{will}}\,{\text{be}}\,{\text{same}}\,{\text{as}} \cr & \frac{{{4^{107}}}}{7} \cr & Or,\,\frac{{{4^3}}}{7} \cr & Or,\,\frac{{64}}{7} \cr & {\text{Required}}\,{\text{Remainder}} = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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