16 fiction books and 20 nonfiction books are to be put in giveaway bags. The number of fiction books in each bag will be the same as the number of nonfiction books in the bag. What is the greatest number of bags that can be made? Jillain says that if the number of fiction books goes up to 18 then the number of bags that can be made will also go up, is she correct? Why or why not?
Mathematics · College · Mon Jan 18 2021
Answered on
Given the statement:
16 fiction books and 20 nonfiction books are to be put in giveaway bags. The number of fiction books in each bag will be the same as the number of nonfiction books in the bag.
Determine the greatest number of bags that can be made.
Solution:
In order to determine the greatest number of bags that can be made, we simply needed to take the greatest common factor of 16 and 20. This can be done by listing the factors of 16 and 20 individually.
Factors of 16:
1, 2, 4, 8, 16
Factors of 20:
1, 2, 4, 5, 10, 20
It can be seen that the greatest common factor is 4, this means that the greatest number of bags to be filled is 4.
If we increase the number of fictions books to 18, then the greatest common factor of 18 and 20 is 2, which is less than that of 16 and 20.
Final answer:
4 bags