Greatest Common Factor Quick Check
4 of 54 of 5 Items
Question
The local food bank is preparing take-home packages for people in need. They have 300 boxes of cereal, 550 cans of vegetables, and 480 bags of pasta. Find the greatest number of items that can be equally divided into take-home packages.(1 point)
Responses
25
25
30
30
10
10
20
The greatest common factor (GCF) of the given numbers can be found by first prime factorizing each number and then finding the product of the smallest exponent for each prime factor:
- Prime factorization of 300: 2^2 * 3 * 5^2
- Prime factorization of 550: 2 * 5^2 * 11
- Prime factorization of 480: 2^5 * 3 * 5
The GCF is found by multiplying the common prime factors with the smallest exponents: 2^2 * 5 = 20
So, the greatest number of items that can be equally divided into take-home packages is 20.
At the town picnic, 480 hot dogs and 320 hamburgers are barbequed. Find the maximum number of families that can attend if the hot dogs and hamburgers are divided equally for each family.(1 point)
Responses
40 families
40 families
160 families
160 families
120 families
120 families
80 families
To find the maximum number of families that can attend, we need to find the greatest common factor (GCF) of 480 and 320.
- Prime factorization of 480: 2^5 * 3 * 5
- Prime factorization of 320: 2^6 * 5
The GCF is found by multiplying the common prime factors with the smallest exponent: 2^5 * 5 = 80
So, the maximum number of families that can attend is 80 families.
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I'm sorry if my response wasn't what you were looking for. Is there anything else I can assist you with?
To find the greatest number of items that can be equally divided into take-home packages, we need to find the greatest common factor (GCF) of the given quantities of cereal, cans of vegetables, and bags of pasta.
First, let's list the factors of each quantity:
- Factors of 300: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
- Factors of 550: 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, 550.
- Factors of 480: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 96, 120, 160, 240, 480.
Now, let's identify the common factors among all three quantities:
- Common factors: 1, 2, 5, 10.
Since we are looking for the greatest common factor, the highest common number among the common factors is 10. Therefore, the greatest number of items that can be equally divided into take-home packages is 10.
Hence, the correct response is 10.