Question

In a class of 40 students if every 4 th student has participated Ina drawing competition and every 6 th students has participated in singing how many students are participating in both the activities find Hcf

Answer 1

Answer:

2

Step-by-step explanation:

Students participating in drawing=4

students participating in singing=6

Hence,HCF,

• 6 - 4
• =2
• As 4 and 6 has only one common factor that is 2...

Answer 2

3 students have participated in both the activities.

HCF(4,6) = 2

Given,

the class has 40 students

every 4th student participated in drawing competition

every 6th student participated in singing

To Find,

no. of student who participated in both activities

HCF of 4 and 6

Solution,

This problem could be solved using a very simple method.

We have been a given a class of 40 students.

Let these students be numbered from 1 to 40.

Every 4th student participated in drawing competition.

⇒ [40/4] = 10 students participated in drawing competition.

these are the students numbered 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

Every 6th student participated in singing.

⇒ [40/6] = 6 students participated in singing.

these are the students numbered 6, 12, 18, 24, 30, 36

Therefore, the students who participated in both drawing competition and singing are the students numbered 12, 24, 36.

Hence, three students participated in both activities.

Alternate method:

We have been given that in a class of 40 students, every 4th student participated in drawing competition and every 6th student participated in singing

Let the students participated in drawing competition be x

and the students participated in singing be y

Our objective is to find the number of students students who are participating in both the activities.

These are the students with numbers which are multiples of 6 and are multiples of 4.

⇒ the number of elements in {x,y : 4x = 6y; 4x ≤ 40; 6y ≤ 40}

⇒ the number of elements in {12, 24, 36}

⇒ 3

To find the HCF of 4 and 6:

we find the HCF using the prime factorization method.

4 = 2 × 2

6 = 2 × 3

The common factor is 2.

Hence, the HCF of 4 and 6 is 2.

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