Question

Question 196

In a school library, there are 780 books of English and 364 books of Science. Ms. Yakang, the librarian of the school wants to store these books in shelves, such that each shelf should have the same number of books of each subject. What should be the maximum number of books in each shelf?

Answer 1

Given, number of English books = 780

and number of Science books = 364

To find the maximum number of books in each shelf, we have to find the HCF of 780 and 364.

$\begin{array}{ccc}& 2& 780\\ & 2& 390\\ & 3& 195\\ & 5& 65\\ & 13& 13\\ & & 1\end{array}\begin{array}{ccc}& 2& 364\\ & 2& 182\\ & 7& 91\\ & 13& 13\\ & & 1\end{array}\begin{array}{}\end{array}$
Prime factorization of 780 $=2\times 2\times 3\times 5\times 13$
Prime factorization of 364 $=2\times 2\times 7\times 13$

Now, HCF of 780 and 364 = $=2\times 2\times 13$ = 52

Hence, the maximum number of books in each shelf = HCF of 780 and 364 = 52.