Question

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

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

Answer 1

The correct option is D 2, 3 and 13

$3^{13}-3^{10}=3^{10}(3^3-1)=3^{10}\left(26\right)$
$=3^{10}\times 2\times 13$
Hence,
$3^{13}-3^{10}$ is divisible by 2, 3 and 13.