Greatest Common Factor Quick Check

Question

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

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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Answer 5

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