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?
To find the greatest number of treat bags Devon can make, we need to find the greatest common factor of 25 and 15. The factors of 25 are 1, 5, and 25. The factors of 15 are 1, 3, 5, and 15. The only factor both numbers share is 5. Therefore, Devon can make 5 treat bags, with each cousin getting 25/5 = <<25/5=5>>5 stickers and 15/5 = <<15/5=3>>3 pieces of fruit. Answer: \boxed{5}.
To find the greatest number of bags Devon can make so that each cousin gets the same number of stickers and the same number of pieces of fruit, we need to find the greatest common divisor (GCD) of the number of stickers and pieces of fruit.
The GCD will represent the maximum number of treat bags Devon can make. In this case, we need to find the GCD of 25 and 15.
To find the GCD, we can use the Euclidean algorithm:
1. Divide the larger number by the smaller number.
25 ÷ 15 = 1 remainder 10
2. Divide the remainder from step 1 by the previous divisor.
15 ÷ 10 = 1 remainder 5
3. Repeat step 2 until the remainder is zero.
10 ÷ 5 = 2 remainder 0
The GCD of 25 and 15 is the divisor from the last non-zero remainder, which is 5.
Therefore, Devon can make a maximum of 5 treat bags so that each cousin gets the same number of stickers and the same number of pieces of fruit.