Question

The number $3^{13}-3^{10}$ is divisible by:

• A. $2$ and $3$ only.
• B. $3$ and $10$ only.
• C. $2,3$ and $10$ only.
• D. All : $2,3$ and $13$

Answer 1

The correct option is D All : $2,3$ and $13$

The expression can be written as $3^{10}(3^3-1)$
$3^{10}\ast 26=3^{10}\ast 2\ast 13$
Thus the number is divisible by 2, 3 and 13 .
Option D.