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

Answer: (D)

Given: $3^{13}-3^{10}$

$3^{13}-3^{10}=3^{10}(3^3-1)=3^{10}\left(26\right)$
$=3^{10}\times 2\times 13$

Clearly, in factorization, $2,3$ and $13$ are the factors of $3^{13}-3^{10}$.
Hence,
$3^{13}-3^{10}$ is divisible by $2,3$ and $13$.

Hence, Option A is correct.