# Product of digits

Let $$F(x)$$ be a function which returns the products of the digits of $$x$$. E.g. $$F(27)=14,F(248)=64$$.

$$A$$ is the sum of $$F(x)$$ over all 2-digit numbers (i.e. $$10 \leq x \leq 99$$)

$$B$$ is the sum of $$F(x)$$ over all 3-digit numbers (i.e. $$101 \leq x \leq 999$$).

Find $$\frac{B}{A}$$

×