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 subject wise and the higher of each stack is the same. How many stacks will be there?

Answer 1

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 = $2^5\times 3$
∴ 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.

∴ Number of stacks = $\frac{336}{48}+\frac{240}{48}+\frac{96}{48}$ = (7 + 5 + 2) = 14