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Objectives The student will be able to: 1. find the prime factorization of a number. 2. find the greatest common factor (GCF) for a set of monomials.

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A prime number is a number that can only be divided by only one and itself. A composite number is a number greater than one that is not prime. Prime or composite? 37 prime 51 composite

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Prime or Composite? 89 1.Prime 2.Composite 3.Both 4.Neither

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1) Find the prime factorization of 84. 84=4 21 =2 2 3 7 2) Find the prime factorization of -210. -210=-1 210 =-1 30 7 = -1 6 5 7 =-1 2 3 5 7

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3) Find the prime factorization of 45a 2 b 3 45a 2 b 3 = 9 5 a a b b b =3 3 5 a a b b b = 3 2 5 a a b b b Write the variables without exponents.

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What is the prime factorization of 48? 1.3 16 2.3 4 4 3.2 2 3 4 4.2 2 2 2 3

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The Greatest Common Factor (GCF) of 2 or more numbers is the largest number that can divide into all of the numbers. 4) Find the GCF of 42 and 60. Write the prime factorization of each number.

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Greatest Common Factor (GCF) The GCF is extremely important when simplifying or reducing fractions.

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4) Find the GCF of 42 and 60. What prime factors do the numbers have in common? Multiply those numbers. The GCF is 2 3 = 6 6 is the largest number that can go into 42 and 60! 42 =2 3 7 60=2 2 3 5

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5) Find the GCF of 40a 2 b and 48ab 4. 40a 2 b = 2 2 2 5 a a b 48ab 4 = 2 2 2 2 3 a b b b b What do they have in common? Multiply the factors together. GCF = 8ab

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What is the GCF of 48 and 64? 1.2 2.4 3.8 4.16

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GREATEST COMMON FACTOR

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