## A jewelry maker will use 24 blue beads and 30 green beads to make necklaces. What are the possible number of necklaces she can make if each

Question

A jewelry maker will use 24 blue beads and 30 green beads to make necklaces. What are the possible number of necklaces she can make if each necklace has the same number of blue and green beads? How many of each type will be on each necklace?

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1 month 2021-09-08T19:04:10+00:00 1 Answer 0

• 1 necklace: 24 blue, 30 green
• 2 necklaces: 12 blue, 15 green (each)
• 3 necklaces: 8 blue, 10 green (each)
• 6 necklaces: 4 blue, 5 green (each)

Step-by-step explanation:

The greatest common factor of 24 and 30 is 6. The divisors of 6 are 1, 2, 3, and 6. Those are the numbers of identical necklaces that might be made from the beads. The number of beads of each color is found by dividing the total number of beads by the number of necklaces being made.

The possible numbers of necklaces are 1, 2, 3 or 6.

The numbers of (blue, green) beads on each will be (24, 30), (12, 15), (8, 10), or (4, 5), respectively.

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The greatest common factor (GCF) is the product of the common prime factors.

24 = 2^3×3

30 = 2×3×5

The prime factors in common are 2 and 3, so the GCF is 2×3 = 6.