Gloria collects stamps. She has 18 bird stamps, 9 flower stamps, and 12 butterfly stamps. For a school project, she will display an equal number of each kind of stamp on small poster boards. What is the greatest number of poster boards Gloria can make if she uses all of the stamps?(1 point) Responses 2 poster boards 2 poster boards 3 poster boards 3 poster boards 6 poster boards 6 poster boards 9 poster boards
To determine the greatest number of poster boards Gloria can make, we need to find the greatest common factor (GCF) of 18, 9, and 12.
The prime factors of 18 are 2*3^2.
The prime factors of 9 are 3^2.
The prime factors of 12 are 2^2*3.
To find the GCF, we take the highest power of each prime number that appears in the factorization of all three numbers.
The highest power of 2 that appears is 2^1.
The highest power of 3 that appears is 3^1.
Therefore, the GCF is 2*3 = 6.
This means that Gloria can make 6 poster boards, each displaying 6 bird stamps, 6 flower stamps, and 6 butterfly stamps. So the correct answer is 6 poster boards.
To find the greatest number of poster boards Gloria can make, we need to find the greatest common divisor (GCD) of 18, 9, and 12.
Let's find the GCD:
The factors of 18 are 1, 2, 3, 6, 9, and 18.
The factors of 9 are 1, 3, and 9.
The factors of 12 are 1, 2, 3, 4, 6, and 12.
The common factors are 1, 3, and 6. The greatest common factor is 6.
Therefore, Gloria can make 6 poster boards.
To find the greatest number of poster boards Gloria can make, we need to find the greatest common divisor (GCD) of the given numbers - 18, 9, and 12. The GCD represents the largest number that divides each of these numbers evenly.
First, let's find the GCD of 18 and 9. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 9 are 1, 3, and 9. The common factors of 18 and 9 are 1 and 3. The greatest common factor between 18 and 9 is 3.
Now, let's find the GCD of 3 and 12. The factors of 3 are 1 and 3. The factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors of 3 and 12 are 1 and 3. The greatest common factor between 3 and 12 is 3.
Now, we have the GCD of all the numbers - 3. This means that Gloria can make equal sets of 3 stamps.
Let's calculate how many sets Gloria can make:
Number of bird stamps = 18
Number of flower stamps = 9
Number of butterfly stamps = 12
To distribute all the stamps equally, we need to divide the number of each kind of stamp by the GCD:
Number of bird stamp sets = 18 / 3 = 6
Number of flower stamp sets = 9 / 3 = 3
Number of butterfly stamp sets = 12 / 3 = 4
Since we cannot have a fraction of a poster board, we need to take the smallest number of sets, which is 3.
Therefore, Gloria can make 3 poster boards by using all of her stamps.