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.
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· 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
· 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)
· 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)
Development
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:
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· 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
· Collect answer from groups
· 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
Follow up
· Ask students to write any three two-digit numbers and find H CF through prime factorization
· Ask students to make three such questions and find H CF through prime factorization
