Cameron is making bead necklaces. He has 90 green beads and 108 blue beads. What is the greatest number of identical necklaces he can make if he wants to use all the beads?
9 * 10 = 90
9 * 12 = 108
To find the greatest number of identical necklaces Cameron can make using all the beads, we need to find the greatest common divisor (GCD) of the number of green beads and the number of blue beads. The GCD represents the largest number that divides both quantities evenly.
To calculate the GCD of 90 and 108, we can use the Euclidean algorithm. Here's how it works:
1. Divide the larger number by the smaller number and find the remainder.
- 108 ÷ 90 = 1 remainder 18
2. Take the divisor (the smaller number) and divide it by the remainder obtained in step 1.
- 90 ÷ 18 = 5 remainder 0
3. The last non-zero remainder obtained in step 2 is the GCD.
- In this case, the GCD of 90 and 108 is 18.
So, the greatest number of identical necklaces Cameron can make using all the beads is 18.