**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**

- Ask the students:

· 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.
- Collect answers from groups.
- 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.

**Follow up **

- Ask students to write any three two-digit numbers and find HCF through prime factorization.