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OUR LESSON

OUR LESSON. Greatest Common Factor. Warm Up. Determine whether each number is prime or composite. 1) 139. Prime. 2) 1700 Composite 3) 17 Prime 4) 333 Composite. Lets review what we have learned in the last lesson.

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OUR LESSON

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  1. OUR LESSON Greatest Common Factor Confidential

  2. Warm Up Determine whether each number is prime or composite 1) 139 Prime 2) 1700 Composite 3) 17 Prime 4) 333 Composite Confidential

  3. Lets review what we have learned in the last lesson When a whole number, greater than one has only 2 factors, 1 and whatever your number is, it is called aPrime Number. When a whole number greater than one has more than 2 factors it is called a Composite Number The numbers 0 and 1 are neither Prime or Composite. Confidential

  4. Review The number 60 is a composite number. It can be written as the product 2 x 2 x 3 x 5. 2, 3 and 5 are factors of 60 and all these factors are prime numbers. We call them prime factors. When we express a number as a product of prime factors, we have actually factored it completely. We refer to this process as prime factorization Confidential

  5. Lets take an Example Factor Tree of 280 • 280 • 2 140 • 2 70 • 2 35 • 7 5 So, the Prime Factorization of 280 expressed as a product of Factors looks like this … 2 x 2 x 2 x 7 x 5 Simplified to: 23 x 7 x 5 7 and 5 are Prime numbers so cannot be factored further Confidential

  6. LetsGetStarted! Greatest Common Factor (GCF) of two or more numbers is the greatest number that is a factor of each number Two methods can be used to find GCF Confidential

  7. Method 1 List the factors of each number. Then identify the common factors. The greatest of these common factors is theGCF Find the GCF of 27 and 36 List all the factors of both the numbers Factors of 27 : 1, 3, 9, 27 Factors of 36 : 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors 1, 3, 9 Thus, the GCF of 27 and 36 is 9 Confidential

  8. Method 2 Write the prime factorization of each number. Then identify all common prime factors Multiply these numbers Their product is the GCF Confidential

  9. Lets take the same example to find the factors of 27 and 36 Write the prime factorization 27 36 3 x 9 3 x 12 3 3 x 3 3 x 4 3 3 2 x 2 Factor Tree method Confidential

  10. Lets take another example Find the GCF of 63 and 42 Method 1 List the factors 63: 1, 3, 7, 9, 21, 63 42: 1, 2, 3, 6, 7, 14, 21, 42 Since the common factors are 1, 3, 7 and 21 the GCF is 21 Confidential

  11. Finding GCF of 63 and 42 Method 2 Write the prime factorization • = 3 x 3 x 7 42 = 3 x 2 x 7 The common prime factors are 3 and 7 so the GCF is 3 x 7 = 21 Confidential

  12. Lets see another Example Find the prime factorization of 45a2b3 45a2b3 = 9 • 5 • a • a • b • b • b = 3 • 3 • 5 • a • a • b • b • b = 32 • 5 • a • a • b • b • b Write the variables without exponents Confidential

  13. Now you try some • Find GCF of the following numbers • 1) Find the GCF of 40a2b and 48ab4 8ab • 2) 160 and 550 10 • 3) 20a2 and 14ab 2a • 36, 24, 144, 96 12 • 15, 25 and 30 5 Confidential

  14. Questions • The GCF of any two numbers is highestof their common factors • Find the GCF of each pair of numbers by listing their common prime factors • 7) 80 and 110 common prime factors : 2, 5 and GCF : 10 • 8)42 and 49 common prime factors: 7 and GCF : 7 • 9) Name a pair of numbers whose GCF is 1 14, 33 • 10) What is the GCF of all numbers in the sequence 12, 24, 36, 48,….?12 Confidential

  15. Break Time Confidential

  16. It's GAME TIME !!!! Click here to play a game Confidential

  17. 1) The school band has 54 members while the choir has 48 members. What is the greatest number of rows that each group and be broken into if the number of rows are the same for the two groups? 48 = 2 x 2 x 2 x 2 x 3 54 = 2 x 3 x 3 x 3 GCF = 2 x 3 = 6 Confidential

  18. 2) What would be the greatest number of crayons in each row of an 8 64 and a 96 crayon box, if all rows have the same number. Find the GCF of 8, 64, 96 8: 2 x 2 x 2 64: 2 x 2 x 2 x 2 x 2 x 2 96: 2 x 2 x 2 x 2 x 2 x 3 The GCF is 2 x 2 x 2 = 8 Thus there will be 8 crayons in each row Confidential

  19. 3) Can the GCF of a set of numbers equal to one of the numbers itself? Explain Yes for the set 2 and 4 The GCF is 2 Confidential

  20. Let us review what we have learnt today Greatest Common Factor of two or more numbers can be defined as the greatest number that is a factor of each number We can find the GCF by using 2 methods Confidential

  21. Method 1 List the factors of each number. Then identify the common factors. The greatest of these common factors is the GCF Method 2 Write the prime factorization of each number. Then identify all common prime factors and find their product, to get the GCF Confidential

  22. Find the GCF of these set of numbers b) 10, 20, 35 a) 66 and 72 GCF 5 GCF 6 c) 9, 11 GCF 1 Confidential

  23. Great Job Done Be sure to practice what you have learned today Confidential

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