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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?
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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 $=\frac{240}{48}+\frac{336}{48}+\frac{96}{48}=5+7+2=14$
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