cameron is making bead necklaces. he has 90 green beads and 108 blue beads. what's the greatest number of identical necklace he can make if he wants to use all the beads

assuming, the 90 green and 108 blue are indistinguishable,

number of arrangements
= 198!/(90!108!)

( which is the same as C(198,108) , too large for my calculator to hold that number. )

Am I misinterpreting the question?

18

I hAt Mo MaTh GoDtHeHeCk

To determine the greatest number of identical necklaces Cameron can make using all the beads, we need to find the greatest common divisor (GCD) of the two numbers of beads he has, which are 90 green beads and 108 blue beads.

One way to find the GCD is to list the factors of each number separately and find the common factors they share.

For 90:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

For 108:
Factors of 108: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

From the two lists, we can see that both 90 and 108 have the common factors: 1, 2, 3, 6, 9, 18.

Among these common factors, the greatest one is 18. Therefore, the greatest number of identical necklaces Cameron can make using all the beads is 18.