Problem: There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. The total number of sections thus formed are?

Solution:

To find the total number of sections that can be formed by dividing the students into either boys or girls, we need to find the highest common factor (HCF) of the number of boys and girls.

Step 1: Find the HCF of 576 and 448

We can use the Euclidean algorithm to find the HCF of 576 and 448.

Step 1.1: Divide the larger number by the smaller number and write the remainder.

576 ÷ 448 = 1 with a remainder of 128

Step 1.2: Divide the smaller number by the remainder from the previous step and write the new remainder.

448 ÷ 128 = 3 with a remainder of 64

Step 1.3: Divide the previous remainder by the new remainder and write the new remainder.

128 ÷ 64 = 2 with a remainder of 0

Since the remainder is 0, we can stop the algorithm. The HCF of 576 and 448 is 64.

Step 2: Divide the number of boys and girls by the HCF

We can divide the number of boys and girls by the HCF to find the number of sections that can be formed.

Number of sections for boys = 576 ÷ 64 = 9

Number of sections for girls = 448 ÷ 64 = 7

Step 3: Find the total number of sections

The total number of sections that can be formed is the sum of the number of sections for boys and girls.

Total number of sections = 9 + 7 = 16

Therefore, the total number of sections that can be formed by dividing the students into either boys or girls is 16.

By HCF, we find that the highest number of boys or girls alone in each section can 64. Number of sections of girls = 448 / 64 = 7 Number of sections of boys = 576 / 64 = 9 Total number of sections = Number of sections of boys Number of sections of girls = 9 7 = 12 Thus, total 12 sections will be formed