11.8. A student was supposed to multiply a three-digit number by a four-digit number (the numbers do not start with 0). Instead of doing so, he simply appended the four-digit number to the right of the three-digit number, obtaining a seven-digit number, which is $N$ times ($N \in \mathbb{Z}$) larger than the correct result.

a) Can $N$ be equal to 2 or 10?

b) Find the largest possible value of $N$.