You have 42 red beads and 56 blue beads. You want to make necklaces with the same number of beads without mixing colors. What is the greatest number of beads each necklace can have?"

Answer 1

To find the greatest number of beads each necklace can have, we need to determine the greatest common divisor (GCD) of the two quantities of beads: 42 red beads and 56 blue beads.

First, we can begin finding the GCD by listing the factors of each number:

Factors of 42:

• 1, 2, 3, 6, 7, 14, 21, 42

Factors of 56:

• 1, 2, 4, 7, 8, 14, 28, 56

Next, we identify the common factors from the lists above:

• Common factors of 42 and 56 are: 1, 2, 7, 14

The greatest common factor is 14.

Thus, the greatest number of beads each necklace can have is 14 beads.

To summarize, you can make necklaces containing 14 beads each using the red and blue beads without mixing colors.