To determine the maximum number of teams that the teacher can form with an equal number of boys and girls such that the number of boys and the number of girls in each team share a greatest common factor (GCF), we first need to find the greatest common divisor of the total number of boys and girls in the class.
The number of boys in the class is 12, and the number of girls is 8.
The factors of these numbers are:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 8: 1, 2, 4, 8
Now, we find the GCF of 12 and 8: The common factors are: 1, 2, 4. The greatest of these is 4.
This means we can divide the class into teams such that each team will have 4 boys and 4 girls. To find out how many teams we can form, we divide the total number of boys and girls by the number that can be in each team.
- Number of teams with boys: \( \frac{12 \text{ boys}}{4 \text{ boys/team}} = 3 \text{ teams} \)
- Number of teams with girls: \( \frac{8 \text{ girls}}{4 \text{ girls/team}} = 2 \text{ teams} \)
Since the limiting factor (the smaller number of teams) is the number of teams we can form with the girls, the teacher can form 2 teams with equal number of boys and girls (4 boys and 4 girls on each team).
Thus, the maximum number of teams that can be created is 2.
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