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Prime Factorization.

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Prime number Composite numbers Prime factorization Factor tree

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Prime number a number that has exactly two factors 1 and itself. 7 13 29 2

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Composite number A number that is not prime A number that has more than two factors 4 (1, 2, 4) 24 (1, 2, 3, 4, 6, 8, 12, 24) 18 (1, 2, 3, 6, 9, 18)

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Prime factorization writing a number as a product of prime numbers.

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Find the prime factorization of 300. 300 3100 10 25253 × × ×××× × The Prime Factorization is 2×2×3×5×5 or 2 2 × 3 × 5 2 3

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Find the prime factorization of 112. 112 256 78 2472 × × ××× × The Prime Factorization is 2×2×2×2×7 or 2 4 × 7 2 2272×××2×

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Find the prime factorization of 324. 324 2162 281 9922 × × ××× × The Prime Factorization is 2×2×3×3×3×3 or 2 2 × 3 4 2 3322×××3×3×

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300112 2×2×3×5×5 2×2×2×2×7 7 2 2 2 2 3 5 5 Make a Venn diagram from the prime factorization of 112 and 300. The GCF is the product of the intersection numbers. (2 × 2 = 4) The LCM is the product of ALL the numbers in the Venn diagram. LCM: 2 × 2 × 2 × 2 × 3 × 5 × 5 × 7 = 8400

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The LCM is the product of ALL the numbers in the Venn diagram. LCM: 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 7 = 9072 The GCF is the product of the intersection numbers. (2 × 2 = 4) 324 112 2×2×3×3×3×3 2×2×2×2×7 7 2 2 2 2 3 3 3 3 Make a Venn diagram from the prime factorization of 112 and 324.

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The GCF is the product of the intersection numbers. (2 × 2 × 3 = 12) The LCM is the product of ALL the numbers in the Venn diagram. LCM: 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 = 8100 324 300 2×2×3×5×5 2×2×3×3×3×3 2 2 3 3 3 3 5 5 Make a Venn diagram from the prime factorization of 324 and 300.

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324 300112 2×2×3×5×5 2×2×3×3×3×3 2×2×2×2×7 7 2 2 2 2 3 3 3 3 5 5

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7530 3×5×52×3×5 3 5 2 5 Make a Venn diagram from the prime factorization of 30 and 75. The GCF is the product of the intersection numbers. (3 × 5 = 15) 215 235 × ×× 325 355 × ×× The LCM is the product of ALL numbers. (2 × 3 × 5 × 5 = 150)

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What does it mean if the Venn diagram of the prime factorizations of two numbers had no numbers in the intersection? Find two numbers that would have a Venn diagram like this.

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Find the prime factorization of -630.

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Homework

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Lesson 10-1: Factors & Greatest Common Factor (GCF)

Lesson 10-1: Factors & Greatest Common Factor (GCF)

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