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

Answer 1

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.