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Factors and Greatest Common Factors (GCF)

8-1. Factors and Greatest Common Factors (GCF). 8-1. A number that has exactly 2 factors, 1 and itself. Prime number:. *2 is the first prime number. Composite number:. A whole number that has more than two factors.

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Factors and Greatest Common Factors (GCF)

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  1. 8-1 Factors and Greatest Common Factors (GCF)

  2. 8-1 A number that has exactly 2 factors, 1 and itself. Prime number: *2 is the first prime number. Composite number: A whole number that has more than two factors. A number is either PRIME or COMPOSITE. It cannot be both.

  3. Let’s find all the prime numbers up to 150…. 8-1 • PLEASE KEEP THIS HANDOUT! YOU WILL BE ABLE TO USE IT ON ALL TESTS/QUIZZES!!!! • YOU GET 1 COPY.

  4. 8-1 Prime factorization: finding which prime numbers multiply together to make the original number. ‌ The method we will use is the: FACTOR TREE ‌ ‌

  5. 8-1 Factor Tree of 48. Steps: 1. Find ANY 2 factors of the original number. (Factors: 2 numbers multiplied together) 2. Find 2 factors of each new number. 3. Continue until you are left with ONLY prime numbers. ANSWER: 24∙3

  6. 8-1 2. Find the prime factorization of -20 1. Find the prime factorization of 90

  7. 8-1 4. Find the prime factorization of -140 3. Find the prime factorization of 42

  8. 8-1 6. Find the prime factorization of -36 5. Find the prime factorization of 56.

  9. 8-1 Greatest Common Factor (GCF): of two or more integers is the greatest number that is a factor of all of the integers. a.k.a: the largest # that will divide into all of the numbers evenly.

  10. 8-1 What is the GCF of the following: • 16 and 24 • 42 and 56 -Factors of 16: -Factors of 24: -Factors of 42: -Factors of 56:

  11. To find on your calculator: 8-1

  12. Find the GCF of each set of monomials. • 3. 30 and 15 • 4. 20 and 60 • 5. 8 and 18 • 26 and 25 • -5 and 15 8-1 15 20 2 1 5

  13. What if you had variables?? Remember the GCF has to be the same thing taken out of both terms! Find the GCF of: 8. x3 and x5 9. x2y2 and xy4 xxx xxxxx GCF: x3 xxyy xyyyy GCF: xy2

  14. 8-1 When variables are involved… Pull out the variables they SHARE. 10. 36x2y and 54xy2 11. 45x3y and 9x2 12. 63x4yz and 48x2y 18xy 9x2 3x2y

  15. 8-1 When variables are involved… Pull out the variables they SHARE. 13. 24x4y2 and 18xy2 14. 100xy and 55x2y2 15. 75x4yz and 15x2yz 6xy2 5xy 15x2yz

  16. When variables are involved… Pull out the variables they SHARE. 8-1 16. 12xy2z and 30xz 17. 17x and 30xy2 18. 18x4 and 15yz 6xz x 3

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