LESSON PLANNING OF FIND HCF OF THREE NUMBERS, UP TO 2 DIGITS, USING DIVISION METHOD

Subject Mathematics

Grade 5^{th}

Students` Learning Outcomes

- Find HCF of three numbers, up to 2 digits, using division method.

Information for Teachers

- There are many methods of finding HCF of two or more numbers, e.g. through prime factorization or through division etc.

- If large numbers are given then it is hard to find all the common prime factors, in such situation, the HCF of these numbers can be found by using division.
- There are two methods of division to find HCF, one by continuous division process and second is Ladder Method.
- In continuous division process, from two given numbers, any one is taken as divisor and other is as dividend, and after division, now remainder is taken as divisor and the first divisor is taken as dividend and we repeat division process. The process keep continue until we get the remainder ‘0’. Hence the last non zero divisor is called GCD or HCF.
- If we have to find HCF of three numbers through continuous division process then first we find the HCF of any two numbers according to the above method, then divide third number with this HCF until we get the remainder ‘0’. Hence the last non zero divisor is our required HCF.
- Find HCF of 12, 45 and 21 through division (Continuous division method).

- Find the HCF of three numbers through division (Ladder Method)
- In this method we write all numbers together and divide only by prime numbers, we select that prime number which divides all the given numbers exactly.
- Tell them that in this process us continuous division tell all the numbers are divisible by single prime number, and then stop dividing further. Hence the product of all prime divisors is called HCF.
- We will use the same example which given above to show that it does n`t matter what method you use and the answer always remains same.
- Find HCF of 12, 45, and 21 through division (Ladder method)

- So these three numbers can`t further divide by single prime number, so HCF of these number is 3.
- During teaching the lesson, the teacher should also consult with textbook when and where applicable.

Material / Resources

Writing board, chalk /marker, duster, textbook

Introduction

- Invite any student on board and ask to do prime factorization of 35, 40 and 20.

- Invite any student on board and ask him to identify common factors.

- Call another student and ask him to find HCF, such as; Common Factor = 5 i.e. HCF = 5
- As there is only one common factor in the given numbers, therefore it is HCF.
- Repeat this activity with different questions and different students.

Ask students;

o What is divisor?

o What is dividend?

o What is quotient?

- Solve any division question on board and ask students to identify divisor, dividend, remainder and quotient.

Development

Activity 1

- Write few two-digit numbers questions on board and ask students to solve on copies.
- When all students have solved the questions, write their answers on board.
- Guide the students in solving questions.
- Inform the students that today we will learn the new method of finding HCF, i.e. HCF by using division method.
- There are two methods of division to find HCF, one by continuous division process and second is Ladder Method.

Activity 2

- Ask students to divide 55 by 40 and tell the remainder?
- Now write the questions on board and find remainder.

- Tell the students, in order to find the HCF of these two numbers through division, now we will keep the divisor inside and divide by remainder.
- Solve the questions on board along with explanation.
- We continue the process until the remainder is ‘0’.

- Tell the students that we find the HCF of these two numbers by continuous division process.
- In this process, the last non zero divisor is called GCD or HCF.

Give students few questions for practice.

Guide the students in solving questions.

Activity 3

- Write 20, 40 and 35 on board.
- Ask students to find HCF of any two of these numbers.
- Now ask them to divide the third number by this HCF until you get the remainder ‘0’.
- Collect the answer from students.
- Conclude that after division with third number, the last non zero divisor is our required HCF.
- Now solve this question on board, so that all students understand this concept.
- Tell the students, now we learn the method of finding HCF of three two-digit numbers by division method.
- For practice give such type of questions to students in groups.

Activity 4

- Tell the students, now we will learn another method of division to find HCF. This is called Ladder Method.
- In this method we write all numbers together and divide only by prime numbers, we select that prime number which divides all the given numbers exactly.
- Tell the students, how to find the HCF of 32, 24, and 40 according to this method.

- Tell them that in this process we continue division till all the numbers are divisible by single prime number, and then stop dividing further. Hence the product of all prime divisors is called HCF, i.e. 2 x 2 x 2 = 8 HCF = 8
- Now ask the students, now in groups find HCF by this method, of those question which were solved by continuous division process so they use, the answer remains same.
- Allocate time to solve questions.
- Guide the students in their work.

Activity 5

- Once you see that they are comfortable with finding HCF through division in pairs, assign them individual questions.
- For example assign question no. 1 to student one, question no. 2 to second student and so on.
- It depends upon the number of questions.
- You may restart from question number 1, 2, 3 etc. when all questions finish.
- Allocate time 15 minutes.
- Now ask students to share their work with each other and correct mistakes.

Sum up / Conclusion

- There are many methods of finding HCF of two or more numbers, e.g. through prime factorization or through division etc.
- If large numbers are given then it is hard to find all the common prime factors, in such situation, the HCF of these numbers can be fund by using division.
- There are two methods of division to find HCF, one by continuous division process and second is Ladder Method.
- Explain both methods of division to find HCF by the method given in the question e.g. by using prime factorization or by using division.
- If ‘find HCF’ is written in the question than you can find HCF by any method but use any one method in one question?

Assessment

- Write on board; find HCF of 9, 65, and 39.
- Now draw following table on board.

- Now ask three students to solve this question on board by all three methods.
- At a time there will be three students attempting question on the board.
- Students observe that, whatever the method use to solve the question, the answer remains same.
- After this write new question and invite three new students.
- Invite such students on board who are less participation in the class.
- At the end, appreciate students through clapping.

Follow up

- Ask students’ to write any three two-digit numbers and find HCF through both methods of division.
- Ask students to make three such questions and find HCF through both methods of division.