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Factoring Numbers

Factoring Numbers. Erica Matulich MTED 301 MW 8:00AM. Idea #1. “Factors” are the numbers you multiply to get another number. Idea #1. Example: Factors of 15 3 and 5 , because 3 x 5 = 15. Idea #1. Some numbers have more than one factorization. Idea #1. Example: 12 12= 1x 12.

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Factoring Numbers

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  1. Factoring Numbers Erica Matulich MTED 301 MW 8:00AM

  2. Idea #1 • “Factors” are the numbers you multiply to get another number.

  3. Idea #1 Example: Factors of 15 3and 5, because 3 x 5= 15

  4. Idea #1 • Some numbers have more than one factorization

  5. Idea #1 • Example: 12 • 12= 1x 12

  6. Idea #1 • Example: 12 • 12= 1x 12 • 12= 2 x 6

  7. Idea #1 • Example: 12 • 12= 1x 12 • 12= 2 x 6 • 12= 3 x 4

  8. Idea #2 • A number that can be factored as 1 times itself is called “prime”

  9. Idea #2 • First few prime numbers are: 2,3,5,7,11,13

  10. Idea #3 • You most often want to find the "prime factorization" of a number.

  11. Idea #3 • Meaning: you want to find the list of all the prime-number factors of a given number.

  12. Idea #3 • For instance, the prime factorization of 8 is 2×2×2, not just "2".

  13. Idea #3 • Yes, 2 is the only factor, but you need three copies of it to multiply back to 8. 2 x 2 x 2 = 8

  14. Idea #4 • Prime factorization includes ONLY the prime factors, not any products of those factors.

  15. Idea #4 • Prime factorization includes ONLY the prime factors, not any products of those factors. • For example: 2×2 = 4

  16. Idea #4 • Prime factorization includes ONLY the prime factors, not any products of those factors. • For example: 2×2 = 4 4 is a divisor of 8

  17. Idea #4 • Prime factorization includes ONLY the prime factors, not any products of those factors. • For example: 2×2 = 4 4 is a divisor of 8 4 is NOT in the PRIME factorization of 8.

  18. Idea #4 • Prime factorization includes ONLY the prime factors, not any products of those factors. • For example: 2×2 = 4 4 is a divisor of 8 4 is NOT in the PRIME factorization of 8. • That is because 8 does NOT equal2×2×2×4!

  19. Idea #4 • Example: The number 24

  20. Idea #4 24 / \ 2 12 / \ 26 / \ 23

  21. Idea #4 2 x 2 x 2 x 3= 24

  22. Idea #4 • Find the prime factorization of 1050

  23. Idea #4 1050 / \ 2 525 / \ 3 175 / \ 5 35 / \ 5 7

  24. Idea #4 Then the answer is:  1050 = 2 × 3 × 5 × 5 × 7

  25. The End • Hope you learned something new and are excited to factor numbers!!

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