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`