Question

In a school 391 boys and 323 girls have been divided into largest possible equal classes, so that each class of boys numbers the same as each class of girls. What is the number of classes?

Answer 1

Hint: We will write the numbers as the product of their prime factors. Then, find their HCF. The HCF of two numbers will be the number of students each class has. Then, divide the number of boys by their HCF to find the number of classes of boys and similarly, find the number of classes of girls. Then, add both the number of classes to find the total number of classes.

Complete step-by-step answer:
There are a total number of 391 boys and 323 girls.
We will find the number of students that will be in each class by determining the HCF of the numbers 391 and 323.
For finding HCF, we will first write the numbers as the product of the prime factors.

17	391
23	23
	1

That is, $391 = 17 \times 23$

17	323
19	19
	1

Hence, $323 = 17 \times 19$
Therefore, the highest common factor of 391 and 323 is 17.
That is, each class will have 17 boys and 17 girls.
Now, we will find the number of classes of boys that will be formed when there are 391 boys
We will divide 391 by 17
$\dfrac{{391}}{{17}} = 23$
Similarly, divide number of classes of girls by 17 to find the number of classes that will be formed when there are 323 girls
$\dfrac{{323}}{{17}} = 19$
Then, we will add both the number of classes to find the total number of classes.
$23 + 19 = 42$


Note: We can also add the number of girls and number of boys to find the total number of students and then divide the total number of students by the HCF to find the total number of classes that can be formed. HCF of the numbers is the largest number that divides the numbers completely.