19. When 2007 bars of soap are packed into $N$ boxes of equal size, where $N$ is an integer strictly between 200 and 300 , there are extra 5 bars remaining. Find $N$.
19. Ans: 286 .
By assumption, $2007-5=N \cdot k$ for some integer $k$. Factorize $2002=2 \cdot 7 \cdot 11 \cdot 13$. Since $200<N<300$, the only possibility is $N=2 \cdot 11 \cdot 13=286$ and $k=7$.