When the number $2^{1000}$ is divided by $13$, the remainder in the division is
$\textbf{(A) }1\qquad \textbf{(B) }2\qquad \textbf{(C) }3\qquad \textbf{(D) }7\qquad  \textbf{(E) }11$
By [Fermat's Little Theorem](https://artofproblemsolving.com/wiki/index.php/Fermat%27s_Little_Theorem), we know that $2^{100} \equiv 2^{1000 \pmod{12}}\pmod{13}$. However, we find that $1000 \equiv 4 \pmod{12}$, so $2^{1000} \equiv 2^4 = 16 \equiv 3 \pmod{13}$, so the answer is $\boxed{\textbf{(C)}}$.