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1. Find the remainder when 4⁹⁶ is divided by 6.

A. 0

B. 2

C. 3

D. 4

Solution:

\frac{4^{96}}{6},

we can write it in this form

\frac{{(6 - 2)}^{96}}{6}

Now, Remainder will depend only the powers of -2. So,

\frac{{(- 2)}^{96}}{6},

it is same as

\frac{{({[- 2]}^{4})}^{24}}{6},

it is same as

\frac{{(16)}^{24}}{6}

Now,

\frac{(16 \times 16 \times 16 \times 16 . . . . . . 24 times)}{6}

On dividing individually 16 we always get a remainder 4.

\frac{(4 \times 4 \times 4 \times 4 . . . . . . 24 times)}{6}

Hence, Required Remainder = 4
NOTE: When 4 has even number of powers, it will always give remainder 4 on dividing by 6.

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