Question

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 minimum number of books in each shelf?

Answer 1

Number of books of English = 780

Number of books of Science = 364

2	780
2	390
3	195
5	65
13	13
	1

 

2	364
2	182
7	91
13	13
	1

780 = 2 × 2 × 3 × 5 × 13

364 = 2 × 2 × 7 × 13

∴ The HCF of 780 and 364 = 2 × 2 × 13 = 52

Thus, the minimum number of books in each shelf = 52