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 subject wise and the higher of each stack is the same. How many stacks will be there?
Total number of English books = 336
Total number of mathematics books = 240
Total number of science books = 96
∴ Number of books stored in each stack = HCF (336, 240, 96)
Prime factorisation:
$336=2^{4} \times 3 \times 7$
$240=2^{4} \times 3 \times 5$
$96=2^{5} \times 3$
$\therefore$ HCF $=$ Product of the smallest power of each common prime factor involved in the numbers $=2^{4} \times 3=48$
Hence, we made stacks of 48 books each.
$\therefore$ Number of stacks $=\frac{336}{48}+\frac{240}{48}+\frac{96}{48}=(7+5+2)=14$
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