Find the remainder when 7 27 16 3 is divided by 10. Options: A . &nbsp7 B . &nbsp9 C . &nbsp1 D . &nbsp3

Find the remainder when 727163 is divided by 10.

Question

Find the remainder when

{7^{27}}^{16}^{3}

is divided by 10.

Options:

A . 7

B . 9

C . 1

D . 3

Answer: Option A
:
A
We need to find out the unit digit of the given number.

\frac{{27^{16}}^{3}}{4} = \frac{27^{e v e n n u m b e r}}{4} = \frac{(- 1)^{e v e n n u m b e r}}{4} = 1

Now the question changes to finding the unit digit of

7^{4 n + 1}

. From the power cycle of 7, unit digit will be 7. Hence, the remainder is 7.

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