PRIME FACTORIZATION GCF

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PRIME FACTORIZATIONGCF LCM
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FACTORING

• Factoring is the opposite of multiplying
• A Factor Times another Factor Equals a Product
• A Composite Number can be factored by
  two or more numbers
• Factoring is breaking Down a Product into its
  Factors
• Prime Factorization is breaking down a Product
  into its Prime Factors.

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FACTOR TREE
A factor tree breaks a product down into its
Prime Factors. It is called PRIME FACTORIZATION
PRODUCT
30
3
10
PRIME FACTORS
3
2
5
4
Prime Factorization
Factor 225
5
Prime Factorization
Factor 225

• Put number on top of factor tree.

225
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Prime Factorization
Factor 225

1. Put number on top of factor tree.
2. Find factors and branch down tree

225
5 45
5 9
5 5 3 3 32 52
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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
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HOW TO FIND THE GCF
The key to determining the GCF is to identify
Common Factors in Both Numbers and Multiplying
them together.
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COMMON FACTORS OF 225 30
225
30
5 45
3 10
5 9
3 5 2
5 5 3 3
THE COMMON FACTORS ARE 5 3
10
IDENTIFY COMMON FACTORS
3 5 2
7 5 2 17
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IDENTIFY COMMON FACTORS
3 5 2
7 5 2 17
THE COMMON FACTORS ARE 5 2
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IDENTIFY COMMON FACTORS
7 5 5 3 3
2 5 2 5 7
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IDENTIFY COMMON FACTORS
7 5 5 3 3
2 5 2 5 7
THE COMMON FACTORS ARE 7 5 5
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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
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IDENTIFY COMMON FACTORS
557

7 5 5 3 3
2 5 2 5 7

2 11 5 3 7
13 3 2 5 2
253
None

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
Only 2 is in common
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Finding Greatest Common Factor
Find GCF of 225 30
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Finding Greatest Common Factor
Find GCF of 225 30
225

1. Complete Factor Tree for both numbers.

30
5 45
3 10
5 9
3 5 2
5 5 3 3
18
Finding Greatest Common Factor
Find GCF of 225 30
225

1. Complete Factor Tree for both numbers.
2. Identify Common Factors.

30
5 45
3 10
5 9
3 5 2
5 5 3 3
THE COMMON FACTORS ARE 5 3
19
Finding Greatest Common Factor
Find GCF of 225 30
225

1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply Common Factors for GCF

30
5 45
3 10
5 9
3 5 2
5 5 3 3
THE COMMON FACTORS ARE 5 3
GCF 5 3 15
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Finding the LCMLeast 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.
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Finding the LCMLeast Common Multiple
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Finding Least Common Multiple
Find LCM of 45 25
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Finding Least Common Multiple
Find LCM of 45 25
45
75

1. Complete Factor Tree for both numbers.

25 3
5 9
5 3 3
5 5 3
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Finding Least Common Multiple
Find LCM of 45 25
45
75

1. Complete Factor Tree for both numbers.
2. Identify Common Factors.

25 3
5 9
5 3 3
5 5 3
THE COMMON FACTORS ARE 5 3
25
Finding Least Common Multiple
Find LCM of 45 25
45
75

1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply Common Factors with ALL OTHER FACTORS

25 3
5 9
5 3 3
5 5 3
THE COMMON FACTORS ARE 5 3
OTHER FACTORS
LCM CFsALL OTHER FACTORS LCM 53 5 3
225
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Finding Least Common Multiple
Find LCM of 12 34

1. Complete Factor Tree for both numbers.
2. Identify Common Factors.
3. Multiply CFs with ALL OTHER FACTORS

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Finding the LCMLeast Common Multiple(FOR 3
NUMBERS)
Find LCM of 225, 10 66
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Finding the LCMLeast Common Multiple(FOR 3
NUMBERS)
Find LCM of 225, 10 66
225

1. Complete Factor Tree for all numbers.

10
66
5 45
5 2
11 6
5 9
11 3 2
5 5 3 3
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Finding the LCMLeast Common Multiple(FOR 3
NUMBERS)
Find LCM of 225, 10 66
225

• Complete Factor Tree for all numbers.
• Identify Common Factors OF ANY 2 S.

10
66
5 45
5 2
11 6
5 9
11 3 2
5 5 3 3
THE COMMON FACTORS ARE 2,5 3
30
Finding the LCMLeast Common Multiple(FOR 3
NUMBERS)
Find LCM of 225, 10 66
225

1. Complete Factor Tree for all numbers.
2. Identify Common Factors OF ANY 2 S.
3. Multiply Common Factors with ALL OTHER FACTORS

10
66
5 45
5 2
11 6
5 9
11 3 2
5 5 3 3
OTHER FACTORS
THE COMMON FACTORS ARE 2,5 3
LCM25353114950