2. (6 points) The remainder when $439 \times 319 \times 2012 + 2013$ is divided by 7 is $\qquad$ .
【Solution】Solution: $(439 \times 319 \times 2012+2013) \div 7$,
$$
\begin{array}{l}
=(439 \times 319 \times 2012+2012+1) \div 7, \\
=[2012 \times(439 \times 319+1)+1] \div 7, \\
=[2012 \times 140042+1] \div 7,
\end{array}
$$

Since 140042 is divisible by 7, the product $2012 \times 140042$ is also divisible by 7. The remainder of 1 divided by 7 is 1, so the remainder when $439 \times 319 \times 2012+2013$ is divided by 7 is 1; hence the answer is: 1.