What is the greatest number of stones marco can
make?
You have to
find the greatest number that divides the three kinds of tiles at the same
time, because this will permit Marco to use the minimum number of each tile and
so he will be able to build the maximum number of stones.
The greatest
number that divides a set of numbers is the greatest common factor (GCF).
To find the
greatest common factor you have to decompose every number in the prime factors
and multiply only the common factors each raised to its lower exponent.
So,
45 = 3^2*5
90 =
2*3^2*5
75 = 3*5^2
The common
factors with their minimum exponents are: 3 and 5. Whose multilplication is 15.
Then the
maximum number of stones is 15.
How many of each color tile will Marco use in
each stone?
Just divide
the number of each stone by 15
Red: 45/15
= 3
Blue: 90/15
= 6
Yellow:
75/3 = 25
How can Marco use the gcf to find out how many
tiles he has in all?
By multiplying
the GCF times the number of tiles in each stone, he will find out how many
tiles of each kind he has in all.
