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**PRIME FACTORIZATION GCF & 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 it’s Factors Prime Factorization is breaking down a Product into it’s Prime Factors.

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FACTOR TREE A factor tree breaks a product down into it’s Prime Factors. It is called PRIME FACTORIZATION PRODUCT 30 3 10 3 • 2 • 5 PRIME FACTORS

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Prime Factorization Factor 225

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Prime Factorization Factor 225 Put number on top of factor tree. 225

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**Prime Factorization Factor 225 Put number on top of factor tree. 225**

Find factors and branch down tree 225 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 3 • 5 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 5 & 3

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**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**

5•5•7 7 • 5 • 5 • 3 • 3 & 2 • 5 • 2 • 5 • 7 2 • 11 • 5 • 3 • 7 & 13 • 3 • 2 • 5 • 2 2•5•3 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 Complete Factor Tree for both numbers. 30 3 • 5 • 2 5 • 5 • 3 • 3

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**Finding Greatest Common Factor**

Find GCF of 225 & 30 225 Complete Factor Tree for both numbers. Identify Common Factors. 30 3 • 5 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 5 & 3

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**Finding Greatest Common Factor**

Find GCF of 225 & 30 225 Complete Factor Tree for both numbers. Identify Common Factors. Multiply Common Factors for GCF 30 3 • 5 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 5 & 3 GCF = 5 • 3 = 15

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**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.

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**Finding the LCM Least 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 Complete Factor Tree for both numbers. 5 • 3 • 3 5 • 5 • 3

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**Finding Least Common Multiple**

Find LCM of 45 & 25 45 75 Complete Factor Tree for both numbers. Identify Common Factors. 5 • 3 • 3 5 • 5 • 3 THE COMMON FACTORS ARE 5 & 3

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**Finding Least Common Multiple**

Find LCM of 45 & 25 45 75 Complete Factor Tree for both numbers. Identify Common Factors. Multiply Common Factors with ALL OTHER FACTORS 5 • 3 • 3 5 • 5 • 3 THE COMMON FACTORS ARE 5 & 3 OTHER FACTORS LCM = CF’s•ALL OTHER FACTORS LCM = 5•3 • 5 • 3 = 225

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**Finding Least Common Multiple**

Find LCM of 12 & 34 Complete Factor Tree for both numbers. Identify Common Factors. Multiply CF’s with ALL OTHER FACTORS

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**Finding the LCM Least Common Multiple (FOR 3 NUMBERS)**

Find LCM of 225, 10 & 66

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**Finding the LCM Least Common Multiple (FOR 3 NUMBERS)**

Find LCM of 225, 10 & 66 225 Complete Factor Tree for all numbers. 10 66 5 • 2 11 • 3 • 2 5 • 5 • 3 • 3

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**Finding the LCM Least 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 • 2 11 • 3 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 2,5 & 3

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**Finding the LCM Least 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. Multiply Common Factors with ALL OTHER FACTORS 10 66 5 • 2 11 • 3 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 2,5 & 3 OTHER FACTORS LCM=2•5•3•5•3•11=4950

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© Boardworks 20101 of 13 Unit 1 – Number Systems GCF and LCM.

© Boardworks 20101 of 13 Unit 1 – Number Systems GCF and LCM.

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