Suppose $656_7=3ab_{10}$, where $a$ and $b$ represent base-10 digits. Find $\frac{a\cdot b}{15}$.
Note that $656_7=6\cdot7^2+5\cdot7^1+6\cdot7^0=335_{10}$. Therefore, $a=3$, $b=5$, and $\frac{a\cdot b}{15}=\frac{3\cdot5}{15}=\boxed{1}$.