Question

Rosy has 16 pencils and 24 erasers. She is putting together packets that will have an equal number of pencils and erasers in each packet. If Rosy uses all of the pencils and erasers, what is the maximum number of packets she can make?

Answer 1

it says she wants to use *all* of the supplies. let's call the "maximum number of packets" x

x can only be a whole, positive number, since it represents the # of packets

additionally, the number of pencils and erasers per packet must also be a whole, positive number

16/x and 24/x must also be integers

therefore, you're really looking for the greatest common factor of 16 and 24. start by listing out factors of 16 (1, 2, 4, etc.) and 24 (1, 2, 3, etc.) and see which is the greatest # common to both lists.