Question

greatest common factor - applications - item 31128
you are making snack bags to sell at the fair. you want each bag to contain the same combination of carrot and celery sticks. you have 75 carrot sticks and 40 celery sticks and want to use them all.
what is the greatest number of snack bags you can make?
3 snack bags
5 snack bags
9 snack bags
15 snack bags

Explanation:

Step1: Find factors of 75

The factors of 75 are \(1, 3, 5, 15, 25, 75\) (since \(1\times75 = 75\), \(3\times25 = 75\), \(5\times15 = 75\)).

Step2: Find factors of 40

The factors of 40 are \(1, 2, 4, 5, 8, 10, 20, 40\) (since \(1\times40 = 40\), \(2\times20 = 40\), \(4\times10 = 40\), \(5\times8 = 40\)).

Step3: Identify common factors

The common factors of 75 and 40 are \(1, 5\).

Step4: Determine the greatest common factor (GCF)

The greatest among the common factors (\(1, 5\)) is 5. So the greatest number of snack bags is 5.

Answer:

5 snack bags