# In a seminar, the number of participants in Hindi, English and Mathematics are 60,84 and 108 respectively. Find the maximum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

By Ruchika|Updated : May 17th, 2023

If in a seminar, the number of participants in Hindi, English, and Mathematics are 60,84, and 108 respectively, and all of them are to be seated in the same subject, then the maximum number of rooms required is 21.

To calculate the number of rooms, we divide the total number of participants in each subject by the maximum number of participants that can be accommodated in a single room. The Highest Common Factor (HCF) is used to determine the maximum number of participants that can be accommodated in a single room.

Solution:

First, you need to find the highest common factor (HCF) of the given numbers to determine the maximum number of participants that can be accommodated in a room.

Prime factorizations of the given numbers are:

60 = 2 x 2 x 3 x 5

84 = 2 x 2 x 3 x 7

108 = 2 x 2 x 3 x 3

The common factors are 2² and 3.

Therefore, the HCM of 60, 84 and 108 is 2² x 3 = 12.

This means that each room can accommodate a maximum of 12 participants.

To find the maximum number of rooms required, we need to divide the total number of participants in each subject by the maximum number of participants that can be accommodated in a room.

For Hindi, the number of rooms required is 60/12 = 5.

For English, the number of rooms required is 84/12 = 7.

For Mathematics, the number of rooms required is 108/12 = 9.

Therefore, the total number of rooms required is:

5 + 7 + 9 = 21 Rooms

Summary:

## In a seminar, the number of participants in Hindi, English, and mathematics are 60,84, and 108 respectively. Find the maximum number of rooms required if in each room the same number of participants are to be seated and all of them being in the same subject.

The total number of rooms required is 21, with 5 rooms for Hindi, 7 rooms for English, and 9 rooms for Mathematics. The HCF method is used to determine the number of rooms required for each subject. HCF stands for Highest Common Factor and it is used to identify the largest factor that divides two or more numbers. In other words, HCF is the largest number that can divide all the given numbers without leaving any remainder.

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