Using Prime Factorization

1
Using Prime Factorization

• Objective To find the GCF and LCM of integers
  and monomials

2
Prime Numbers

• An integer greater than 1 whose only factors are
  its self and one.
• Examples 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
• Real life application cryptography (code
  breaking)

3
Example

• Find the prime factorization of 432
• 432 216 2
• 108 2 2
• 54 2 2 2
• 27 2 2 2 2
• 9 3 2 2 2 2
• 3 3 3 2 2 2 2
• 33 24

4
Greatest Common Factor (GCF)

• The greatest integer that is a factor of each
  integer.
• Example find the GCF of 27 and 117
• 27 3 3 3, 117 13 3 3
• GCF 3 3 9

5
Least Common Multiple (LCM)

• Least positive integer having each as a factor
• Example Find the least common multiple of 27 and
  117
• 27 3 3 3 33, 117 13 3 3 13 32
• Take the largest factors of each number
• LCM 33 13 351

6
Try These! find the GCF and LCM

1. 80 and 12
2. 110 and 33
3. 45, 100, and 70
4. 16a4b3 and 12a2b
5. 21a2b5, 14a3b3, and 35a2b2

• 4, 240
• Solution
• 11, 330Solution
• 5, 6300Solution
• 4a2b, 48a4b3Solution
• 7a2b2, 210a3b5Solution

End Show
7
80 and 12

• 80 40 2
• 80 20 2 2
• 80 10 2 2 2
• 80 5 2 2 2 2
• 80 5 24
• 12 6 2
• 12 3 2 2
• 12 3 22

• GCF 4
• LCM 5 24 3 240

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8
110 and 33

• 110 11 5 2
• 33 3 11

• GCF 11
• LCM 11 5 2 3LCM 330

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9
45, 100, and 70

• 45 32 5
• 100 52 22
• 70 7 5 2

• GCF 5
• LCM 6300

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10
16a4b3 and 12a2b

• 16a4b3 24 a4 b3
• 12a2b 22 3 a2 b

• GCF 22 a2 bGCF 4a2b
• LCM 24 3 a4 b3LCM 48a4b3

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11
21a2b5, 14a3b3, and 35a2b2

• 21a2b5 73a2b5
• 14a3b3 72a3b3
• 35a2b2 75a2b2

• GCF 7a2b7a2b
• LCM 7523a3b5LCM 210a3b5

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