Devon is making treat bags to pass out to his cousins at the next family party. He has 25 stickers and 15 pieces of fruit. He wants each of the treat bags to have the same number of stickers. He also wants each of the treat bags to have equal numbers of pieces of fruit. He does not want to have any stickers or pieces of fruit left over. What is the greatest number of bags he can make so that each cousin gets the same number of stickers and the equal number of pieces of fruit?(1 point)
The greatest number of bags is
5
The greatest number of bags that Devon can make is equal to the greatest common divisor (GCD) of 25 and 15. To find the GCD, we can list the factors of each number and find their common factors.
Factors of 25: 1, 5, 25
Factors of 15: 1, 3, 5, 15
The common factors are 1 and 5. Therefore, the greatest common divisor is 5.
So, Devon can make a maximum of 5 bags where each cousin gets the same number of stickers and the same number of pieces of fruit.
To find the greatest number of treat bags Devon can make, where each bag has the same number of stickers and pieces of fruit, you need to find the greatest common divisor (GCD) of the number of stickers and the number of pieces of fruit.
Step 1: Find the GCD
- The number of stickers is 25 and the number of pieces of fruit is 15.
- List all the factors of both numbers:
- Factors of 25: 1, 5, 25
- Factors of 15: 1, 3, 5, 15
- The common factors are 1 and 5.
- The GCD is the largest common factor, which is 5.
Step 2: Find the number of bags
- To find the greatest number of bags, divide the number of stickers and pieces of fruit by the GCD:
- Number of bags = Number of stickers / GCD = 25 / 5 = 5
- Number of bags = Number of pieces of fruit / GCD = 15 / 5 = 3
So, Devon can make 5 treat bags where each cousin gets 5 stickers and 3 pieces of fruit.