Answer:
- 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)
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.