Question

The digit in the unit place of the number $\angle 183+3^{183}$ is

• A. 0
• B. 3
• C. 6
• D. 7

Answer 1

Answer: (D)

$3^1=3\Rightarrow$ unit's place = 3
$3^2=9\Rightarrow$ unit's place = 9
$3^3=27\Rightarrow$ unit's place = 7
$3^4=81\Rightarrow$ unit's place = 1
$3^5=243\Rightarrow$ unit's place = 3
Continuing this process $3^{183}=(3^4{)}^{45}\cdot 3^3$
$\therefore$ Unit's place = $1\times 7=7=7$
Unit's place of $183!=0$
Hence, unit's place of $183!+3^{183}=0+7=7.$