Samantha is making beaded necklaces using 54 glass beads and 18 clay beads. She wants each necklace to have the same number of beads, but each necklace will have only one type of bead. If Samantha puts the greatest possible number of beads on each necklace, how many necklaces can she make?

To determine how many necklaces Samantha can make, we need to find the greatest common divisor (GCD) of the number of glass beads and clay beads.

The GCD, also known as the highest common factor (HCF), is the largest number that divides two or more numbers evenly.

In this case, the GCD will represent the maximum number of beads each necklace can have. Let's calculate it:

1. Find the factors of the number of glass beads (54):
- The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

2. Find the factors of the number of clay beads (18):
- The factors of 18 are 1, 2, 3, 6, 9, and 18.

3. Determine the common factors:
- The common factors of 54 and 18 are 1, 2, 3, 6, and 9.

4. Identify the largest common factor, which is the GCD:
- The greatest common divisor (GCD) of 54 and 18 is 9.

Therefore, Samantha can make a maximum of 9 necklaces, each with 9 beads (either glass or clay).

If she puts the greatest possible number of beads on each necklace, Samantha can make 8 necklaces?