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.
2 poster boards
3 poster boards
6 poster boards
9n poster boards
To find the greatest number of poster boards Gloria can make, we need to find the greatest common divisor (GCD) of the number of each type of stamp.
The GCD of 18, 9, and 12 is 3.
Therefore, Gloria can make 3 poster boards, with an equal number of each kind of stamp on each board.
To find the greatest number of poster boards Gloria can make, we need to find the greatest common factor of the three numbers: 18, 9, and 12.
The prime factorization of 18 is 2 * 3 * 3.
The prime factorization of 9 is 3 * 3.
The prime factorization of 12 is 2 * 2 * 3.
Taking the highest exponent for each prime factor, the greatest common factor is 2 * 3 * 3 = 18.
Therefore, Gloria can make 18 poster boards using all of the stamps.
To find the greatest number of poster boards Gloria can make, we need to determine the greatest common divisor (GCD) of the number of stamps for each kind.
First, let's list the numbers of stamps Gloria has for each kind:
- Bird stamps: 18
- Flower stamps: 9
- Butterfly stamps: 12
Now, let's find the GCD of these numbers.
We can start by finding the GCD of 18 and 9:
- Divide 18 by 9: 18 ÷ 9 = 2
Since the remainder is 0, 9 is a divisor of 18, and the GCD of 18 and 9 is 9.
Next, let's find the GCD of 9 and 12:
- Divide 12 by 9: 12 ÷ 9 = 1 (remainder 3)
- Divide 9 by 3: 9 ÷ 3 = 3
Again, since the remainder is 0, 3 is a divisor of 9, and the GCD of 9 and 12 is 3.
Finally, let's find the GCD of 3 and 3:
- Divide 3 by 3: 3 ÷ 3 = 1
Since the remainder is 0, 3 is a divisor of 3, and the GCD of 3 and 3 is 3.
So the greatest common divisor (GCD) of the number of stamps for each kind is 3.
To determine the greatest number of poster boards Gloria can make, we need to divide the total number of stamps by the GCD:
- Total number of stamps = 18 + 9 + 12 = 39
- Number of poster boards = Total number of stamps ÷ GCD = 39 ÷ 3 = 13
Therefore, Gloria can make a maximum of 13 poster boards if she uses all of the stamps.