Question

How can Marco use the gcf to find out how many tiles he has in all?

Answer 1

GCF is the greatest number that distributes the three kinds of tiles at the same time, because this will let Marco to use the least number of each tile and so he will be capable to form the maximum number of stones. To find the greatest common factor you have to decompose each number in the prime factors and multiply only the common factors each raised to its lower exponent.For example: 45, 90, and 75 are the given:45 = 3^2*5
90 = 2*3^2*5
75 = 3*5^2
The common factors with their minimum exponents are: 3 and 5, the product would be 15. Thus the maximum number of stones is 15. By multiplying the GCF times the sum of tiles in each stone, he will find out how many tiles of each type he has in total.