# Lesson Plan of H CF up to 2 digits using Prime Factorization Method Mathematics Grade V

#### Students’ Learning Outcomes

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

#### Information for Teacher

·         H.C.F.: The highest common factors (H.C.F.) of two or more given numbers are the greatest which divides each of given numbers exactly.
·         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.
E.g. 12 = 2x 2 x 3
o   Factors shared by two or more numbers are called common factors. E. g.
o   Because ‘2’ is common in factors of both of these numbers so it is called common factor.
o   The product of two or more common prime factors is the greatest number/factor, which is called Greatest Common Divisor (GCD) or highest Common Factor (H CF).
o   Highest common factor ‘H CF’ of two or more numbers is the greatest number that divides each one of given numbers exactly.
o   Method of prime factorization for finding H CF of two or more numbers.

#### Step 1:

o   Express each one of the given number 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 is called (GCD) or highest Common factor (H CF).
·         Find the H CF of 16, 36, and 52 using factorization method.
·

·         In this example ‘4’ is the H CF or GCD which divides 16, 36, and 52 exactly.
·         During teaching the lesson, teacher should concern with textbook, when and where necessary in all steps.

#### Material / Resources

Board, marker/chalk, duster, basket or box, paper slips having topic relevant questions on it, textbook

#### Worm up activity

o   What are prime numbers?
(Expected response: such numbers which are divisible by 1 and itself)
o   What are composite numbers?
(Expected response: such numbers have at least one more factor other than 1 and itself)
o   Which are prime numbers?
(Expected response: write on board such as 2, 3, 5, 7, 11, 13, 17 etc.)
o   Which are composite numbers?
(Expected response: write on board such as 4, 6, 8, 9, 10, 12, 14, 15, 16 etc.)
o   Why it is prime or composite number? (by writing any number)
·         Check students understanding by talking discussion along with few examples of numbers.
·         Also repeat the term ‘Factor’ every time you discuss about a number. For example ‘12’ is composite because it has factors more than one, (which are 2, 3, 4, 6 and 12)
o   What are ‘Factors’?
(Expected response: the number which divides any number exactly is called its factor)
o   What are prime factors?
(Expected response: such factors of any number which are prime, are called prime factors)
o   Which are the prime factors of number 14?
(Expected response: 2, 7)
o   Which are the composite factors of number 18?
(Expected response: 6, 9, 18)
o   What do you mean by prime factorization?
o   What will be the prime factorization of number 16?
(Expected response: 2 x2 x 2 x 2)
o   What do you know about H CF?
(Expected response: H CF of two or more numbers is the greatest number that divides each one of them exactly)
o   What does H CF stand for?
(Expected response: Highest Common Factor)

#### Activity 1

·         Ask 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 H CF.
·         Let the students think themselves.
·         Collect answers from different students.
·         Now demonstrate the method as explained in ‘information for teacher’
·         Now ask students to find H CF of 84 and 28:
·
·         Now give students, more two– digit questions for practice.

#### Activity 2

·         Write any three numbers on board e.g. 27, 45, 63
·         Now divide students in groups
·         Ask students to find H CF according to the method learn
·         Don’t tell the students, let them think
·         Now solve this question on board and tell the students, the method of finding H CF of three numbers
·         For practice, give students; further two-digit numbers to solve in groups
·         Conclude that we have learned the method of finding H CF of three-digit numbers through prime factorization

#### Activity 3

·         Once you see that they are comfortable with finding H CF through factorization 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

#### Activity 4

·         Write different questions on board
·         Ask students to find H CF according to the method learn
·         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 participate 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 either prime nor composite)
·         Prime factorization means to express a number as the product of its prime factors.
·          E.g. 12 = 2 x 2 x 3
·         Factors shared by two or more numbers are called common factors e.g.
·         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 Divisor (GCD) or Highest common Factor (H CF)
·         Highest Common Factor ‘H CF’  of two or more numbers is the greatest number that divides each one of given numbers exactly
·         Tell the students, the method of finding H CF through prime factorization and solve few questions on the board #### Assessment

·         Put paper slips of questions in a basket or box and shuffle it
·         Go to different students, especially those who are less participate 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 THUMBS UP, if answer is wrong then THUMBS DOWN
·         This will help you check how many of the students understand this concept
·         Sample questions for writing on slips  as such:
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 H CF of 12 and 24?
o   Find the H CF of 76, 56, and 20 through prime factorization