8 1 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. *2 is the first prime number. A whole number that has more than two factors. A number is either PRIME or COMPOSITE. It cannot be both.

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

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

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

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

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

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

8 -1 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.

8 -1 What is the GCF of the following: 1. 16 and 24 -Factors of 16: -Factors of 24: 2. 42 and 56 -Factors of 42: -Factors of 56:

8 -1 To find on your calculator:

8 -1 Find the GCF of each set of monomials. 30 and 15 15 4. 20 and 60 20 5. 8 and 18 2 6. 26 and 25 1 7. -5 and 15 5

What if you had variables? ? Find the GCF of: 8. x 3 and x 5 xxxxx Remember the GCF has to be the same thing taken out of both terms! GCF: x 3 9. x 2 y 2 and xy 4 xxyy xyyyy GCF: xy 2

8 -1 When variables are involved… Pull out the variables they SHARE. 10. 36 x 2 y and 54 xy 2 18 xy 11. 45 x 3 y and 9 x 2 12. 63 x 4 yz and 48 x 2 y 3 x 2 y

8 -1 When variables are involved… Pull out the variables they SHARE. 13. 24 x 4 y 2 and 18 xy 2 6 xy 2 14. 100 xy and 55 x 2 y 2 5 xy 15. 75 x 4 yz and 15 x 2 yz

8 -1 When variables are involved… Pull out the variables they SHARE. 16. 12 xy 2 z and 30 xz 6 xz 17. 17 x and 30 xy 2 x 18. 18 x 4 and 15 yz 3