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)

Question

The greatest number of bags is

Answer 1

To determine the greatest number of treat bags that Devon can make while ensuring that each bag has the same number of stickers and the same number of pieces of fruit, we need to find the greatest common divisor (GCD) of the total number of stickers and pieces of fruit he has.

Devon has:

• 25 stickers
• 15 pieces of fruit

Now, we need to find the GCD of 25 and 15.

Step 1: Prime factorization

• The prime factorization of 25 is \(5^2\).
• The prime factorization of 15 is \(3^1 \times 5^1\).

Step 2: Identify common factors The only common prime factor is 5.

Step 3: Calculate GCD The minimum power of the common prime factor (5) in both factorizations is \(5^1\).

Thus, the GCD of 25 and 15 is 5.

Therefore, the greatest number of bags Devon can make is 5.

So, the greatest number of bags is \( \boxed{5} \).