Question

Esteban is shopping for a bookshelf. He has 58 non-fiction books and 145 fiction books. He wants each shelf to have the same number of books and to have only one type of book on each shelf. If Esteban wants the greatest possible number of books on each shelf, how many shelves should the bookshelf have?

Answer 1

7

Explanation:

Criteria:

• same number of books on each shelf

⇒find a number that divides 58 and 145

• greatest number of books on each shelf

⇒find the greatest number that divides 58 and 145

Find the GCF of 58 and 145.

58 = 2 ⋅ 29

145 = 5 ⋅ 29The GCF of 58 and 145 is 29.

Each shelf will contain 29 books.

There are 203 total books (because 58 + 145 = 203).

Divide 203 by 29 to find the number of shelves there should be.

203 / 29 = 7

Therefore, there will be 7 shelves.