Question

Three sets of English, mathematics and science books containing 336,240 and 96 books respectively have to be stacked in such a way that all the books are stored subjectwise and the height of each stack in the same. How many stacks will be there?

Answer 1

Given : three sets of English, Mathematics and science books containing 336,240 and 96 books respectively
Find the HCF of 336,240 and 96 using prime factorization:
\[
\begin{aligned}
&336=2 \times 2 \times 2 \times 2 \times 3 \times 7=2^{4} \times 3 \times 7 \\
&240=2 \times 2 \times 2 \times 2 \times 3 \times 5=2^{4} \times 3 \times 5 \\
&96=2 \times 2 \times 2 \times 2 \times 3=2^{5} \times 3
\end{aligned}
\]
\[
\mathrm{HCF}=2^{4} \times 3=16 \times 3=48
\]
each stack of book will contain 48 books .
Thus, the number of stacks \(=\frac{240}{48}+\frac{336}{48}+\frac{96}{48}=5+7+2=14\)