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Prime Factorization

Prime Factorization. Used to find the LCM and GCF to help us add and subtract fractions. Factors. A factor is a number that divides another number with no remainder. Examples: factors of 12 are 1 & 12, 2 & 6, 3 & 4. Prime numbers. A number that has only two factors, 1 and itself.

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Prime Factorization

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  1. Prime Factorization Used to find the LCM and GCF to help us add and subtract fractions.

  2. Factors • A factor is a number that divides another number with no remainder. • Examples: factors of 12 are 1 & 12, 2 & 6, 3 & 4

  3. Prime numbers • A number that has only two factors, 1 and itself. • Examples: 2, 3, 5, 7, 11, 13, 17…

  4. Prime Factorization • The prime factorization of a number is the product of its prime factors. • Example: of 12- or

  5. Factor Trees • Use a factor tree to break down a number to get to the prime numbers (till you can’t break it down anymore) or

  6. Another example

  7. One more example…

  8. Now you try … • Find the prime factorization of: • 40 • 48

  9. GCF The Greatest Common Factor between at least two numbers… used to simplify fractions.

  10. GCF • The greatest common factor of two or more numbers is the greatest factor that is in common to those numbers. • The GCF can be found by: • Listing all the factors of each number and then finding the largest number in all lists to give the GCF. • Do a factor tree of each number and the prime factors that are in all trees multiply to give the GCF.

  11. Listing all the factors… • This works best when the numbers are small and have few factors. • 12 and 15 • Factors of 12: 1, 2, 3, 4, 6, 12 • Factors of 15: 1, 3, 5, 15 • GCF= 3

  12. Do a factor tree… • This works best when the numbers are large and have many factors. These two trees share a 3 and 5. Multiply these two together and get 15. GCF=15

  13. Try another with a factor tree • 45 and 81 • GCF=3x3=9

  14. Now you try… Find the GCF • 16 and 24 • 12, 48, 72

  15. LCM Least Common Multiple between at least two numbers… used to find a common denominator to help add and subtract fractions.

  16. Multiple • The multiple of a number is a product of that number and a whole number… • Meaning multiply! • Multiples of 5: • 5, 10, 15, 20, 25, 30… • Multiples of 3: • 3, 6, 9, 12, 15, 18, 21…

  17. LCM • Least Common Multiple is the smallest multiple of two or more numbers. • The easiest way to find the LCM: • Start to list all the multiples of the numbers involved and stop as soon as you have a number in common to both lists. • Ex: between 3 and 5 • 5, 10, 15, 20… • 3, 6, 9, 12, 15… • So the LCM is 15!

  18. You try it! • Find the LCM between 4 and 9 • Make a list of multiples of each number. • 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 • 9, 18, 27, 36.. • LCM = 36!

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