Question

Hiya has 60 English books, 75 Hindi books, and 105 Gujarati books. She wants to arrange them on shelves such that

Each shelf contains books of only one language.
All shelves contain the same number of books.
What is the largest number of books that she can place in one shelf?

Answer 1

To find the largest number of books that Hiya can place in one shelf, we need to determine the greatest common divisor (GCD) of the three given numbers: 60, 75, and 105.

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

The factors of 75 are: 1, 3, 5, 15, 25, 75.

The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105.

From these lists, we can see that the common factors among the three numbers are 1 and 3. Therefore, the largest number of books that Hiya can place in one shelf is 3.

Explanation: