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PRIME FACTORIZATION GCF & LCM
FACTORING <ul><li>Factoring is the opposite of multiplying </li></ul><ul><li>A Factor Times another Factor Equals a Produc...
FACTOR TREE A factor tree breaks a product down into it’s Prime Factors. It is called PRIME FACTORIZATION  30 3 10 3  • 2 ...
Prime Factorization Factor  225
Prime Factorization Factor  225 <ul><li>Put number on top of factor tree.  </li></ul>225
Prime Factorization Factor  225 <ul><li>Put number on top of factor tree.  </li></ul><ul><li>Find factors and branch down ...
GCF - Greatest Common Factor The GCF  of two numbers is the greatest number that divides into both numbers evenly. Ex: The...
HOW TO FIND THE GCF The key to determining the GCF is to identify Common Factors in Both Numbers and Multiplying them toge...
COMMON FACTORS OF 225 & 30 THE COMMON FACTORS ARE 5 & 3 225 5  45 5  9 5  •  5  •  3  •  3  3  10 30 3  •  5  •  2
IDENTIFY COMMON FACTORS 3  •  5  •  2 7  •  5  •  2 • 17
IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 5 & 2 3  •  5  •  2 7  •  5  •  2 • 17
IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 7 & 5 & 5 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7 & 2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2 & 3 • 5 • 11 • 3 • 3 2...
IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7 & 2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2 & 3 • 5 • 11 • 3 • 3 2...
Finding Greatest Common Factor Find GCF of 225 & 30
Finding Greatest Common Factor 225 5  45 5  9 5  •  5  •  3  •  3  3  10 30 3  •  5  •  2 Find GCF of 225 & 30 <ul><li>Com...
Finding Greatest Common Factor THE COMMON FACTORS ARE 5 & 3 225 5  45 5  9 5  •  5  •  3  •  3  3  10 30 3  •  5  •  2 Fin...
Finding Greatest Common Factor THE COMMON FACTORS ARE 5 & 3 225 5  45 5  9 5  •  5  •  3  •  3  3  10 30 3  •  5  •  2 Fin...
Finding the LCM Least Common Multiple The LCM is the Lowest Number that is a Multiple of Both Numbers. Ex. The LCM of 12 &...
Finding the LCM Least Common Multiple
Finding Least Common Multiple Find LCM of 45 & 25
Finding Least Common Multiple 45 5  9 5  •  3  •  3  5  •  5 • 3 25  3 Find LCM of 45 & 25 <ul><li>Complete Factor Tree fo...
Finding Least Common Multiple THE COMMON FACTORS ARE 5 & 3 45 5  9 5  •  3  •  3  5  •  5 • 3 25  3 Find LCM of 45 & 25 <u...
Finding Least Common Multiple THE COMMON FACTORS ARE 5 & 3 45 5  9 5  •  3  •  3  5  •  5 • 3 25  3 Find LCM of 45 & 25 <u...
Finding Least Common Multiple Find LCM of 12 & 34 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identif...
Find LCM of 225, 10 & 66 Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul>Finding the LCM Least Common Multiple (FO...
Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul><ul><li>Identify Common Factors OF ANY 2 ...
Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul><ul><li>Identify Common Factors OF ANY 2 ...
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Gcf&Lcm

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Transcript of "Gcf&Lcm"

  1. 1. PRIME FACTORIZATION GCF & LCM
  2. 2. FACTORING <ul><li>Factoring is the opposite of multiplying </li></ul><ul><li>A Factor Times another Factor Equals a Product </li></ul><ul><li>A Composite Number can be factored by two or more numbers </li></ul><ul><li>Factoring is breaking Down a Product into it’s Factors </li></ul><ul><li>Prime Factorization is breaking down a Product into it’s Prime Factors. </li></ul>
  3. 3. FACTOR TREE A factor tree breaks a product down into it’s Prime Factors. It is called PRIME FACTORIZATION 30 3 10 3 • 2 • 5 PRODUCT PRIME FACTORS
  4. 4. Prime Factorization Factor 225
  5. 5. Prime Factorization Factor 225 <ul><li>Put number on top of factor tree. </li></ul>225
  6. 6. Prime Factorization Factor 225 <ul><li>Put number on top of factor tree. </li></ul><ul><li>Find factors and branch down tree </li></ul>225 5 45 5 9 5 • 5 • 3 • 3 = 3 2 • 5 2
  7. 7. GCF - Greatest Common Factor The GCF of two numbers is the greatest number that divides into both numbers evenly. Ex: The GCF of 14 & 35 is 7, since 7 is the greatest number that goes into both 14 & 35 evenly
  8. 8. HOW TO FIND THE GCF The key to determining the GCF is to identify Common Factors in Both Numbers and Multiplying them together.
  9. 9. COMMON FACTORS OF 225 & 30 THE COMMON FACTORS ARE 5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 3 10 30 3 • 5 • 2
  10. 10. IDENTIFY COMMON FACTORS 3 • 5 • 2 7 • 5 • 2 • 17
  11. 11. IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 5 & 2 3 • 5 • 2 7 • 5 • 2 • 17
  12. 12. IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
  13. 13. IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 7 & 5 & 5 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7
  14. 14. IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7 & 2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2 & 3 • 5 • 11 • 3 • 3 2 • 2 • 2 • 17 • 7 & 5 • 5 • 7 • 3 2 • 5 • 2 • 3 & 2 • 5 • 2 • 7 & For three numbers common factors must be in all three numbers
  15. 15. IDENTIFY COMMON FACTORS 7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7 & 2 • 11 • 5 • 3 • 7 13 • 3 • 2 • 5 • 2 & 3 • 5 • 11 • 3 • 3 2 • 2 • 2 • 17 • 7 & 5 • 5 • 7 • 3 2 • 5 • 2 • 3 & 2 • 5 • 2 • 7 & For three numbers common factors must be in all three numbers 5•5•7 2•5•3 None Only 2 is in common
  16. 16. Finding Greatest Common Factor Find GCF of 225 & 30
  17. 17. Finding Greatest Common Factor 225 5 45 5 9 5 • 5 • 3 • 3 3 10 30 3 • 5 • 2 Find GCF of 225 & 30 <ul><li>Complete Factor Tree for both numbers. </li></ul>
  18. 18. Finding Greatest Common Factor THE COMMON FACTORS ARE 5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 3 10 30 3 • 5 • 2 Find GCF of 225 & 30 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identify Common Factors. </li></ul>
  19. 19. Finding Greatest Common Factor THE COMMON FACTORS ARE 5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 3 10 30 3 • 5 • 2 Find GCF of 225 & 30 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identify Common Factors. </li></ul><ul><li>Multiply Common Factors for GCF </li></ul>GCF = 5 • 3 = 15
  20. 20. Finding the LCM Least Common Multiple The LCM is the Lowest Number that is a Multiple of Both Numbers. Ex. The LCM of 12 & 9 is 36 since both 12 & 9 divide evenly into 36. Hint: Think of Common Denominators in Fractions. A common denominator is the LCM of the denominators.
  21. 21. Finding the LCM Least Common Multiple
  22. 22. Finding Least Common Multiple Find LCM of 45 & 25
  23. 23. Finding Least Common Multiple 45 5 9 5 • 3 • 3 5 • 5 • 3 25 3 Find LCM of 45 & 25 <ul><li>Complete Factor Tree for both numbers. </li></ul>75
  24. 24. Finding Least Common Multiple THE COMMON FACTORS ARE 5 & 3 45 5 9 5 • 3 • 3 5 • 5 • 3 25 3 Find LCM of 45 & 25 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identify Common Factors. </li></ul>75
  25. 25. Finding Least Common Multiple THE COMMON FACTORS ARE 5 & 3 45 5 9 5 • 3 • 3 5 • 5 • 3 25 3 Find LCM of 45 & 25 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identify Common Factors. </li></ul><ul><li>Multiply Common Factors with ALL OTHER FACTORS </li></ul>LCM = CF’s•ALL OTHER FACTORS LCM = 5•3 • 5 • 3 = 225 75 OTHER FACTORS
  26. 26. Finding Least Common Multiple Find LCM of 12 & 34 <ul><li>Complete Factor Tree for both numbers. </li></ul><ul><li>Identify Common Factors. </li></ul><ul><li>Multiply CF’s with ALL OTHER FACTORS </li></ul>
  27. 27. Find LCM of 225, 10 & 66 Finding the LCM Least Common Multiple (FOR 3 NUMBERS)
  28. 28. Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul>Finding the LCM Least Common Multiple (FOR 3 NUMBERS) 225 5 45 5 9 5 • 5 • 3 • 3 11 6 66 11 • 3 • 2 5 • 2 10
  29. 29. Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul><ul><li>Identify Common Factors OF ANY 2 #’S. </li></ul>Finding the LCM Least Common Multiple (FOR 3 NUMBERS) THE COMMON FACTORS ARE 2,5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 11 6 66 11 • 3 • 2 5 • 2 10
  30. 30. Find LCM of 225, 10 & 66 <ul><li>Complete Factor Tree for all numbers. </li></ul><ul><li>Identify Common Factors OF ANY 2 #’S. </li></ul><ul><li>Multiply Common Factors with ALL OTHER FACTORS </li></ul>OTHER FACTORS Finding the LCM Least Common Multiple (FOR 3 NUMBERS) THE COMMON FACTORS ARE 2,5 & 3 225 5 45 5 9 5 • 5 • 3 • 3 11 6 66 11 • 3 • 2 5 • 2 10 LCM=2•5•3•5•3•11=4950
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