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 factorisation:

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