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A science museum makes gift bags for students using 168 magnets, 48 robot figurines, and 24 packs of freeze-dried ice cream. How many of each item are in each gift bag?

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sqdancefan

Answer:

  • 7 magnets
  • 2 robot figurines
  • 1 pack of freeze-dried ice cream

Step-by-step explanation:

The greatest common factor of 24, 48, and 168 is 24, so 24 gift bags can be made. Each will have 1/24 of the number of gift items of each type that are available.

In each bag are ...

  • 1/24 × 168 magnets = 7 magnets
  • 1/24 × 48 robot figurines = 2 robot figurines
  • 1/24 × 24 packs of ice cream = 1 pack of ice cream

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One way to find the greatest common factor (GCF) is to consider whether the smallest number divides all the numbers. If so (as here), then that is the GCF. If not, then consider the smallest difference between any pair of numbers, to see if it divides all of the numbers. If not, then test the smallest positive remainder from any of those divisions. Repeat until you have found a common divisor (which may be 1).

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