LESSON PLANNING OF HCF

Students` Learning Outcomes

• Find HCF of three numbers up to 2 digits, using prime factorization method.

Information for Teachers

• Factorization means to express a number as the product of its factors. These factors are either composite numbers or prime numbers. (Except that 0 and 1 are neither prime nor composite).
• Prime factorization means to express a number as the product of its prime factors, such as; 12 = 2 x 2 x 3.
• Factors shared by two or more numbers are called common factors, such as; img
• Because ‘2’ is common in factors of both of these numbers so it is called common factor.

• The product of two or more common prime factors is the greatest number / factor, which is called Greatest Common Divisors (GCD) or Highest Common Factors (HCF)
• Highest Common Factor ‘HCF’ of two or more numbers is the greatest number that divides each one of given numbers exactly.

• Method of prime factorization for finding of HCF of two or more numbers;

Step 1:

o   Express each one of the given numbers as the product of prime factors.

Step 2:

o   Identify the prime factors which are common in all factorization.

Step 3:

o   Now multiply all these prime factors which are common.

o   Thus a number / factor obtained are called (GCD) or Highest Common Factor (HCF).

• Find the HCF of 16, 36 and 52 using prime factorization method.
• In this example ‘4’ is the HCF or GCD which divides 16, 36, and 52 exactly.
• During teaching the lesson, the teacher should also concern with text book, when and where necessary in all steps.

Material / Resources

Writing board, chalk / marker, duster, basket or box, paper slips having topic relevant questions on it, text book

Introduction

·         What are prime numbers? (Such numbers which are divisible by 1 and itself)

·         What are composite numbers? (Such numbers have at least one more factor other than 1 and itself)

·         Which are prime numbers? (Write on board: 2, 3, 5, 7, 11, 13, 17 etc.)

·         Which are composite numbers?  (Write on board: 4, 6, 8, 9, 10, 12, 14, 15, 16, etc.)

• ·         Why it is prime or composite number? (by writing any number) (Check students understanding by taking discussion along with few examples of numbers).
• Also repeat the term ‘Factor’ every time you discuss about a number, such as; ‘12’ is composite because it has factors more than one, which are 2, 3, 4, 6, and 12).

·         What are ‘Factors’? (The number which divides any number exactly is called its factors)

·         What are prime factors? (Such factors of any number which are prime, are called prime factors)

·         Which are the prime factors numbers 14? (2, 7)

·         Which are the composite factors of number 18? (6, 9, 18)

·         What do you mean by prime factorization?

·         What will be the prime factorization of number 16? (2 x 2 2 x 2 x 2)

·         What do you know about HCF? (HCF of two or more numbers is the greatest number that divides each one of them exactly.

·         What does HCF stand for? (Highest Common Factor)

Development

Activity 1

• Ask the students to work in pairs.
• Ask students to find prime factors of 24 and write them as product.
• Now ask students to find prime factors of 48 and write them as product.
• Now ask them to find HCF.
• Let the students think themselves.
• Collect answers from different students.
• Now demonstrate the method as explained in ‘Information for Teachers’
• Now ask students to find HCF of 84 and 28.

• Now give students more two-digit questions for practice.

Activity 2

• Write any three numbers on board such as; 27, 45, 63.
• Now divide students in groups.
• Ask students to find HCF according to the method learns.
• Don`t tell the students, let them think.
• Now solve these questions on board and tell the students, the method of finding HCF of three numbers.
• For practice, give students; further two-digit numbers to solve in groups.
• Conclude that we have learned the method of finding HCF of three-digit numbers through prime factorization.

Activity 3

• Once you see that they are comfortable with finding HCF of three-digit numbers through prime factorization.
• 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.

Activity 4

• Write different questions on board.
• Ask students to find HCF according to the method learns.
• Allocate time 15 minutes.
• Now invite different students on board one by one and ask them to solve and explain.
• Invite such students on board who are less participation in the class.
• At the end, appreciate students through clapping.
Sum up / Conclusion
• Factorization means to express a number as the product of its factors. These factors are either composite numbers or prime numbers. (Except that 0 and 1 are neither prime nor composite).

• Prime factorization means to express a number as the product of its prime factors, such as; 12 = 2 x 2 x 2 x 3
• Factors shared by two or more numbers are called common factors such as; img
• Because ‘2’ is common in factors of both of these numbers so it is called common factor.
• The products of two or more common prime factors are the greatest number / factor, which is called Greatest Common Divisor (GCD) or Highest Common Factor (HCF).
• Highest Common Factor ‘HCF’ of two or more numbers is the greatest number that divides each one of given numbers exactly.
• Tell the students, the method of finding HCF through prime factorization and solve few questions on board.
Assessment
• Put paper slips of questions in a basket or box and shuffle it.
• Go to different students, especially those who are less participation in the class.
• Ask each student to pick the slip and read the question aloud.
• Give them time to think and write answer.
• After this students announce their answer one by one.
• The whole class is the judge.
• If the answer is correct, they will ‘THUMP UP’, if answer is wrong, ‘THUMP DOWN’

• This will help you check how many of the students understand this concept.
• Sample questions for writing on slips;

o   What are factors?

o   What is greatest common factor called?

o   What are common factors?

o   How do you find the highest common factor of two or three numbers?

o   How do you find the HCF of 12 and 24?

• o   Find the HCF of 76, 56, and 20 through prime factorization.