A school library has 84 storybooks and 126 puzzle books. They are to be stacked so that every stack holds the same number of books and each stack contains only one kind of book. With the greatest possible stack size, how many books are in a stack and how many stacks are formed?

**Theorem**: A rational number $\frac{p}{q}$ (in lowest terms) has a terminating decimal expansion if and only if $q$ has the form **2ᵐ × 5ⁿ** (m, n ≥ 0).

**Examples**:
- $\frac{3}{8}:q=8=2^3$ → terminates$.(\frac{3}{8}=\mathrm{0.375.})-\frac{7}{40}:q=40=2^3\times 5$ → terminates$.(\frac{7}{40}=\mathrm{0.175.})-\frac{1}{3}:q=3$ → does NOT terminate$.(\frac{1}{3}=0.333$… recurring.)
- $\frac{4}{15}:q=15=3\times 5$ → does NOT terminate (because of the 3).

**Why**: any decimal expansion is a fraction with denominator 10ⁿ = 2ⁿ × 5ⁿ. To convert $\frac{p}{q}$ to decimal form, you need $q$ to ONLY have 2s and 5s as primes — otherwise you can't multiply numerator/denominator into a power of 10.