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Prime Factorization.

Prime Factorization. Prime number Composite numbers Prime factorization Factor tree. Prime number. a number that has exactly two factors 1 and itself. 7 13 29 2. Composite number. A number that is not prime A number that has more than two factors 4 (1, 2, 4)

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Prime Factorization.

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  1. Prime Factorization.

  2. Prime number • Composite numbers • Prime factorization • Factor tree

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

  4. 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)

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

  6. Find the prime factorization of 300. The Prime Factorization is • 300 3 × 100 3 × 10 × 10 2×2×3×5×5 or 22 × 3 × 52 3 × 2 × 5 × 2 × 5

  7. Find the prime factorization of 112. The Prime Factorization is • 112 2 × 56 2 × 7 × 8 2×2×2×2×7 or 24 × 7 2 × 7 × 2 × 4 2 × 7 × 2 × 2 × 2

  8. Find the prime factorization of 324. The Prime Factorization is • 324 2 × 162 2 × 2 × 81 2×2×3×3×3×3 or 22 × 34 2 × 2 × 9 × 9 2 × 2 × 3 × 3 × 3 × 3

  9. 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 3 2 7 2 5 2 5 2 112 300 2×2×3×5×5 2×2×2×2×7

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

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

  12. 324 2×2×3×3×3×3 3 3 3 3 2 7 2 5 2 5 2 112 300 2×2×3×5×5 2×2×2×2×7

  13. Make a Venn diagram from the prime factorization of 30 and 75. The GCF is the product of the intersection numbers. (3 × 5 = 15) The LCM is the product of ALL numbers. (2 × 3 × 5 × 5 = 150) 30 75 3 2 × 15 3 × 25 5 2 5 2 × 3 × 5 3 × 5 × 5 2×3×5 3×5×5

  14. 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.

  15. Find the prime factorization of -630.

  16. Homework

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