A jewelry designer is making identical bracelets. She has 21 blue beads and 14 red beads. What is the greatest number of bracelets she can make using all of the beads

What is the greatest common factor of 14 and 21

15

To find the greatest number of bracelets that can be made using all of the beads, we need to determine the common factor of 21 and 14.

The greatest common factor (GCF) of 21 and 14 is 7.

Now, let's calculate how many bracelets can be made using this common factor:
- The number of blue beads that can be used = 21 beads ÷ 7 beads per bracelet = 3 bracelets.
- The number of red beads that can be used = 14 beads ÷ 7 beads per bracelet = 2 bracelets.

Since both colors have the same number of bracelets, the maximum number of bracelets that can be made using all of the beads is 2 bracelets.

To find the greatest number of bracelets the jewelry designer can make using all of the beads, we need to determine the common factors of 21 and 14.

Step 1: Find the factors of 21
The factors of 21 are 1, 3, 7, and 21.

Step 2: Find the factors of 14
The factors of 14 are 1, 2, 7, and 14.

Step 3: Determine the common factors
The common factors of 21 and 14 are 1 and 7.

Step 4: Find the greatest common factor (GCF)
The greatest common factor of 21 and 14 is 7.

Step 5: Divide the total number of beads by the GCF
To find the greatest number of bracelets, divide the total number of beads (21 + 14 = 35) by the GCF (7).

35 beads ÷ 7 (GCF) = 5 bracelets

Therefore, the jewelry designer can make a maximum of 5 bracelets using all of the beads. Each bracelet will have 3 blue beads (21 ÷ 7) and 2 red beads (14 ÷ 7).