Question

Find the last 3 digits of ${25}^{63}\times {63}^{25}$.

• A. $3,7,5$
• B. $4,7,5$
• C. $3,4,5$
• D. $2,7,5$

Answer 1

Answer: (A)

$3,7,5$

The last three digits of 25 for power
${25}^1=025$
${25}^2=625$
${25}^3=15625$
For any power of 25 (except 1) the last three digits end with 625
$lastthreedigitsof{25}^{63}=625$
$Now625\times 63=39375\Rightarrow lastthreedigits=375$
$lastthreedigitsof625\times {63}^n=375$
$ifnisodd$
$\therefore Thelastthreedigitsof{25}^{63}\times {63}^{25}\Rightarrow 375$