Question

The digit in the unit place of $2009!+3^{7886}$ is

• A. 9
• B. 7
• C. 3
• D. 1

Answer 1

Answer: (A)

Unit's digit of $2009!=0$
Now, $3^1=3\Rightarrow$ unit's digit = 3
$3^2=9\Rightarrow$ unit's digit = 9
$3^3=27\Rightarrow$ unit's digit = 7
$3^4=81\Rightarrow$ unit's digit = 1
$3^5=243\Rightarrow$ unit's digit = 3
Continuing the process, we get
$3^{7866}=3^{7860+6}=3^{4\times 1965}\times 3^6$
$\therefore$ Unit's digit of $3^{7866}$
= unit's digit of $(3^{4\times 1965}\times 3^6)$
$=(1{)}^{1965}\times 9=9$
So, unit's digit of $2009!+3^{7866}=0+9=9$