John is packing cookies for Key club's bake sale. He has 48 chocolate chips cookies and 56 peanut butter cookies. What is the maximum number of bags he can make?

Answers

Answer 1

The maximum number of bags is an illustration of the greatest common factor

The maximum number of bags John can make is 8

The given parameters are:

[tex]Chocolate=48[/tex]

[tex]Peanut=56[/tex]

Start by expressing 48 and 56 as a product of their factors.

[tex]Chocolate = 1 \times 2 \times 2 \times 2 \times 2 \times 3[/tex]

[tex]Peanut = 1 \times 2 \times 2 \times 2 \times 7[/tex]

The product of the common factors between the above products is:

[tex]Factors = 1 \times 2 \times 2 \times 2[/tex]

Multiply

[tex]Factors = 8[/tex]

The above represents the greatest common factor of 48 and 56.

Hence, the maximum number of bags John can make is 8

Read more about greatest common factor at:

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Answer 2

Step-by-step explanation:

To determine the maximum number of bags John can make, we need to find the greatest common divisor (GCD) of the two quantities: 48 chocolate chip cookies and 56 peanut butter cookies.

The GCD is the largest number that divides both quantities without leaving a remainder. It represents the maximum number of bags that can be made, with each bag containing an equal number of cookies of each type.

Let's find the GCD of 48 and 56:

Step 1: List the divisors of each number:

Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Divisors of 56: 1, 2, 4, 7, 8, 14, 28, 56

Step 2: Identify the common divisors in both lists:

Common divisors of 48 and 56: 1, 2, 4, 8

Step 3: Determine the greatest common divisor (GCD):

The greatest common divisor of 48 and 56 is 8.

So, John can make a maximum of 8 bags, with each bag containing an equal number of chocolate chip and peanut butter cookies.

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