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
The greatest number of poster boards Gloria can make is 3.
To find out the greatest number of poster boards Gloria can make, we need to find the greatest common divisor (GCD) of the numbers of each kind of stamp she has.
The GCD of 18, 9, and 12 is 3.
Therefore, Gloria can make 3 poster boards by displaying an equal number of each kind of stamp on each board.
To determine the greatest number of poster boards Gloria can make, we need to find the common factor among the numbers 18, 9, and 12.
First, we can write the prime factorization of each number:
18 = 2 * 3^2
9 = 3^2
12 = 2^2 * 3
Now, we look for the highest power of each prime factor that appears in all three numbers. In this case, the common factor is 3^2.
Since Gloria needs to display an equal number of each kind of stamp on each poster board, she can arrange 3^2 = 9 bird stamps, 3^2 = 9 flower stamps, and 3^2 = 9 butterfly stamps on each board.
Next, we divide the total number of each type of stamp by the number of stamps on each board to find out how many boards Gloria will need:
For bird stamps: 18 / 9 = 2 boards
For flower stamps: 9 / 9 = 1 board
For butterfly stamps: 12 / 9 = 1 board
Since we want to find the greatest number of poster boards, we choose the maximum number of boards required among the three types, which is 2 boards.
Therefore, the greatest number of poster boards Gloria can make if she uses all of the stamps is 2 poster boards.