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 height 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 factorization: 

336 = 2⁴ × 3 × 7 

240 = 2⁴ × 3 × 5 

96 = 2⁵ × 3 

∴ HCF = Product of the smallest power of each common prime factor involved in the numbers = 2⁴ × 3 = 48 

Hence, we made stacks of 48 books each

Number of stacks = 336/48 + 240/48 + 96/48 = (7+5+2) = 14