Question

There are 576 boys and 448 girls in a school that are divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
1) 24
2) 23
3) 16
4) None of these

Answer 1

Hint: We want to find the highest positive number that divides the total number of boys and the total number of girls. So, we will use HCF to find the highest positive number that divides the total number of boys and the total number of girls. This will give us the number of students in the single section. Finally, we will calculate the total sections formed by dividing the total students by the number of students in the single section.

Complete step-by-step answer:
We are given that the total number of boys present is 576 and the total number of girls present is 448.
We want to divide the students into the sections such that each section contains an equal number of students.
Also, a section so formed must either contain all boys or all girls.
Therefore, the number of students must be chosen so that divides the total number of boys and the total number of girls completely.
For this, we will find the number that divides the total number of boys and the total number of girls. So, we will use HCF to find the highest positive number that divides the total number of boys and the total number of girls. This will give us the number of students in the single section.
We shall start by factorising the given numbers.
The number 576 can be factorised as,
$576 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$
The number 448 can be factorised as,
$448 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7$
Write the common factors of the given numbers.
$2 \times 2 \times 2 \times 2 \times 2 \times 2$
Multiply the common factors to determine the highest common factor (HCF) of the given numbers.
$2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64$
Since the highest common factor (HCF) of the given numbers is 64, this implies that each section will have 64 number of students.
Now, we need to find the number of sections formed.
Let us first find the number of sections formed by the total number of boys by dividing 576 by 64.
$\dfrac{{576}}{{64}} = 9$
Now, find the number of sections formed by the total number of girls by dividing 448 by 64.
$\dfrac{{448}}{{64}} = 7$
Thus, the total number of sections formed will be 9+7=16
Hence, option C is the correct answer.

Note: In this question, we have to find a number that divides both the given numbers completely, hence, we will find HCF and not LCM. Many students make mistakes by calculating LCM for the given question. At last, it is important to add the sections formed by boys and girls only to determine the total number of sections formed.