Martha has 90 red tiles and 72 yellow tiles. She wants to place the tiles in rows using one color for each row without having any tiles left over. Each row must have the same number of tiles. What is the greatest number of tiles Martha can use for each row?

18 tiles

Step-by-step explanation:

If she wants to find the greatest number of tiles for each row, she will want to use up all the tiles. This means we are looking for the highest common factor between the numbers 90 and 72, so all the tiles can be used up in the rows. In order to find the highest common factor we multiply together all the common prime factors between the two:

90 has the prime factors 2x3x3x5

72 has the prime factors 2x2x2x3x3

The prime factors that are common to both are 2, 3 and 3 which multiply together to get:

2x3x3 = 18

The greatest number of tiles Martha can use for each row is 18 and would result in 5 rows of red tiles and 4 rows of yellow tiles.

Hope this helped!