If 27 999 is divided by 7, then the remainder is

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Question: Answered & Verified by Expert

If

{(27)}^{999}

is divided by

7,

then the remainder is

MathematicsMathematical InductionJEE Main

Options:

A $1$
B $2$
C $3$
D $6$

Solution:

1165 Upvotes Verified Answer

The correct answer is:

6

Express the given number

27^{999}

as

{(28 - 1)}^{999}

Now, divide by

7,

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

and apply the formula of binomial expansion.
We get the reminder as

- 1 \Rightarrow 7 + (- 1) = 6

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