How many divisors does $2013^{13}$ have? (As usual, we count 1 and $2013^{13}$ itself as divisors, but not negative integers.)
The prime factorization of 2013 is $3 \cdot 11 \cdot 61$, so

$$
2013^{13}=3^{13} \cdot 11^{13} \cdot 61^{13} \text {. }
$$

A divisor of this number is found by choosing 0 to 13 of the factors 3 (there are 14 possible choices), 0 to 13 of the factors 11 (14 choices), and 0 to 13 of the factors 61 (14 choices). So the total number of divisors is $14 \cdot 14 \cdot 14=2744$.