Question

Three sets of English, Hindi and Mathematics books have to be stacked in such a way that all the books are stored topic wise and the height of each stack is the same. The number of English books is 96, the number of Hindi books is 240 and the number of Mathematics books is 336. Assuming that the books are of the same thickness, determine the number of stacks of English, Hindi and Mathematics books.

Answer 1

Hint: In this question, we need to understand that if we want to stack all the book topic wise and with the same height then we need to find the Highest Common factor of all the number of books as we need to find the largest number that divides the given numbers. This will help us simplify the question and reach the answer.

Complete step-by-step answer:
We want to stack all the book topic wise and with the same height. So, we need to find the Highest Common factor of 96, 240 and 336 as we need to find the largest number that divides the given numbers.
The prime factorization of 96, 240 and 336 is
$
  96 = {2^5} \times 3 \\
  240 = {2^4} \times 3 \times 5 \\
  336 = {2^4} \times 3 \times 7 \\
$
So, The HCF of 96, 240 and 336 is$ = {2^4} \times 3 = 48$.
Hence, there will be 48 books in each stack.
Therefore,
The Number of Stacks of English books$ = \dfrac{{96}}{{48}} = 2$
The Number of Stacks of Hindi books$ = \dfrac{{240}}{{48}} = 5$
The Number of Stacks of Mathematics books$ = \dfrac{{336}}{{48}} = 7$
Hence, there will be 2, 5, 7 stacks of the English, Hindi and Mathematics books.

Note: Whenever we face such types of problems the key point is to identify this question based on the highest common factor. In this question students may forget to find out the value of stacks.