Question

What is the unit digit in the product $(3^{65}\times 6^{59}\times 7^{71})$?

• A. $1$
• B. $2$
• C. $4$
• D. $6$

Answer 1

Answer: (C)

$4$

Unit digit in $3^4=1$ $\Rightarrow$ Unit digit in ${\left(3^4\right)}^{16}=1$
$\therefore$ Unit digit in $3^{65}=$Unit digit in ${\left(3^4\right)}^{16}=(1\times 3)=3$
Unit digit in $6^{59}=6$
Unit digit in $7^4=1$ $\Rightarrow$ Unit digit in ${\left(7^4\right)}^{17}=1$
Unit digit in $7^{71}=$ Unit digit in $[{\left(7^4\right)}^{17}\times 7^3]=(1\times 3)=3$
Required digit$=$ Unit digit in $(3\times 6\times 3)=4$