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How many three-digit numbers are divisible by $13$ ? (2004 AMC 8 Problem, Question \#18) 
Overseas Competition->Knowledge Point->Number Theory Modules
Let $k$ be any positive integer so that $13 k$ is a multiple of 13 . For the smallest three-digit number, $13 k\textgreater100$ and $k\textgreater\frac{100}{13} \approx 7.7$. For the greatest three-digit number, $13 k\textless999$ and $k\textless\frac{999}{13} \approx 76.8$. The number $k$ can range from 8 to 76 so there are $(\mathbf{C}) 69$ threedigit numbers. 