QJEEM17Ma677a: JEE Main 2017 Mathematics - Class 11 JEEM17Ma677a Solution: If (27) 999 is divided by 7, then the remainder is :

Question

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If (27)⁹⁹⁹ is divided by 7, then the remainder is :

Accepted Answer

We have,

\frac{{(27)}^{999}}{7}

=

\frac{{(28 - 1)}^{999}}{7}

=

\frac{28 λ - 1}{7}

=

\frac{28 λ - 7 + 7 - 1}{λ}

=

\frac{7 (4 λ - 1) + 6}{7}

∴

Remainder = 6

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