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  • The digit in the unit place of the number  is<div class='qna-optio

The digit in the unit place of the number (183 !)+3^{183} is

Option: 1

7


Option: 2

6


Option: 3

3


Option: 4

0


Answers (1)

best_answer

We know that n! terminates in 0 for n ≥ 5 and 3^{4n} terminator in 1, (3^{4}=81)

\therefore 3^{180}=\left(3^4\right)^{45} terminates in 1
Also 3^3 = 27 terminates in 7
\therefore 3^{183}=3^{180} 3^3  terminates in 7

\therefore 183 !+3^{183}   terminates in 7

i.e. the digit in the unit place  = 7.
 

Posted by

manish painkra

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