You are making balloon arrangements for a birthday party. There are 16 white balloons and 24 red balloons. Each arrangement must be identical. What is the greatest number of arrangements you can make using every balloon?

the GCF (greatest common factor) of 16 and 24 is 8

8 is the greatest number of identical arrangements ... 3 red and 2 white

To find the greatest number of arrangements using every balloon, we need to determine the smallest common factor of 16 and 24, which represents the maximum number of identical arrangements that can be made.

First, let's find the prime factors of 16 and 24:

Prime factors of 16: 2 * 2 * 2 * 2 = 2^4
Prime factors of 24: 2 * 2 * 2 * 3 = 2^3 * 3

Next, let's determine the common factors:

Common factors: 2^3 = 8

Therefore, the greatest number of identical arrangements you can make is 8.

To find the greatest number of arrangements using every balloon, we need to determine the common factors of 16 and 24. The common factors will represent the number of identical arrangements we can make.

First, let's find the factors of 16: 1, 2, 4, 8, 16
Next, let's find the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The common factors of 16 and 24 are 1, 2, 4, and 8. These numbers represent the number of identical arrangements we can make using every balloon.

Therefore, the greatest number of arrangements we can make using every balloon is 8.