#### Students’ Learning Outcomes

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

*Information for Teacher*

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*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.*

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*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).*

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*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).*

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*Find the H CF of 16, 36, and 52 using factorization method.*

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*In this example ‘4’ is the H CF or GCD which divides 16, 36, and 52 exactly.*

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*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 *

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*Ask the students:*

*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)*

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*Check students understanding by talking discussion along with few examples of numbers.*

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*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)*

*Development*

#### Activity 1

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*Ask students to work in pairs.*

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*Ask students to find prime factors of 24 and write them as product.*

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*Now ask students to find prime factors of 48 and write them as product.*

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*Now ask them to find H CF.*

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*Let the students think themselves.*

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*Collect answers from different students.*

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*Now demonstrate the method as explained in ‘information for teacher’*

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*Now ask students to find H CF of 84 and 28:*

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*·*

*Now give students, more two*

*– digit questions for practice.*

*Activity 2*

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*Write any three numbers on board e.g. 27, 45, 63*

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*Now divide students in groups*

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*Ask students to find H CF according to the method learn*

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*Don’t tell the students, let them think*

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*Collect answer from groups*

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*Now solve this question on board and tell the students, the method of finding H CF of three numbers*

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*For practice, give students; further two-digit numbers to solve in groups*

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*Conclude that we have learned the method of finding H CF of three-digit numbers through prime factorization*

*Activity 3*

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*Once you see that they are comfortable with finding H CF through factorization in pairs, assign them individual questions*

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*For example assign question no. 1 to student one, question no. 2 to second student and so on*

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*It depends upon the number of questions*

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*You may restart from question number 1, 2, 3 etc. when all questions finish*

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*Allocate time 15 minutes*

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*Now ask students to share their work with each other and correct mistakes*

*Activity 4*

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*Write different questions on board*

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*Ask students to find H CF according to the method learn*

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*Allocate time 15 minutes*

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*Now invite different students on board one by one and ask them to solve and explain*

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*Invite such students on board who are less participate in the class*

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*At the end, appreciate students through clapping*

*Sum up / Conclusion*

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*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*

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*Put paper slips of questions in a basket or box and shuffle it*

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*Go to different students, especially those who are less participate in the class*

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*Ask each student to pick the slip and read the question aloud*

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*Give them time to think and write answer*

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*After this students announce their answer one by one*

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*The whole class is the judge*

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*If the answer is correct, they will THUMBS UP, if answer is wrong then THUMBS DOWN*

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*This will help you check how many of the students understand this concept*

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*Sample questions for writing on slips as such:*

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*What are factors?*

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*What is greatest common factor called?*

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*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*

*Follow up*

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*Ask students to write any three two-digit numbers and find H CF through prime factorization*

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*Ask students to make three such questions and find H CF through prime factorization*