The sixth-grade class is competing in the school field day. there are 32 girls and 24 boys who want to participate. each team must have the same number of girls and boys. what is the greatest number of teams that can be formed? how many boys and how many girls will be on each team?

Here we need to find common factors between two numbers.

We will see that the maximum number of teams that can be formed is 8, such that each one has 3 boys and 4 girls.

We know that there are:

And we need to separate them in groups, and we need to find the maximum number of groups that can be formed, to get that, we need to find the maximum common factor of 24 and 32.

To get that we can write both of these as a product of prime numbers:

24 = 2*2*2*3

32 = 2*2*2*2*2

In both of these we have 3 times the factor 2, so the largest common factor between 24 and 32 is:

2*2*2 = 8

This means that the maximum number of teams that can be formed is 8.

The number of boys in each team will be:

24/8 = 3

The number of girls in each team will be:

32/8 = 4

If you want to learn more, you can read:

link

8 teams each team will have 4 girls and 4 boys

Step-by-step explanation:

We use GCD to solve this

the GCD of 32 and 24 = 8

8 is the greatest number of teams.

each team must have equal number of boys and girls so divided by two

8/2 = 4

4 girls and 4 boys

I have attached how to do GCD.

If you need any clarification or more explanation pls do mention at the comment section

Hope this helps and if it does pls mark as brainliest answer thx