Problem: The integer $n$ is the smallest positive multiple of $15$ such that every digit of $n$ is either $8$ or $0$. Compute $\frac{n}{15}$. Solution: Since $15 \mid n$, we know that $3 \mid n$ and $5 \mid n$. Since $5 \mid n$, the last digit must be $0$ instead of $8$. Since $3 \mid n$, it follows that the sum of the digits must be divisible by $3.$ The least number of $8s in the number is hence 3, so $ n = 8880 \implies \frac{8880}{15} = 592 .$