Final answer:
The question seeks the total number of sections with equal numbers of boys or girls. To find this, we calculate the greatest common divisor (GCD) for the number of boys and girls, getting 16 sections in total. The correct answer is option (c).
Step-by-step explanation:
The question involves finding the highest number of sections into which 576 boys and 448 girls can be divided, with each section containing only boys or only girls. The total number of sections can be determined by finding the greatest common divisor (GCD) for the number of boys and girls separately, and then adding the two results together.
To find the GCD of 576 boys, we list down the factors of 576 and, similarly, list down the factors of 448 for the girls. The largest common factor in both lists will be the GCD for each gender. Let's break down both numbers into their prime factors:
- 576 = 26 × 32
- 448 = 26 × 7
Since both numbers share a factor of 26, this is the GCD for both groups. So, 576 boys can be divided into 576 / 64 = 9 sections, and 448 girls can be divided into 448 / 64 = 7 sections.
Adding both gives us the total number of sections: 9 (boys) + 7 (girls) = 16 sections.
The correct answer is: c. 16