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 $183! + 3^{183} = 0 + 7 = 7.$