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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 30 310 3 2 5 PRODUCT PRIME FACTORS

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Prime Factorization Factor 225

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Prime Factorization Factor 225 1.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 = 3 2 5 2

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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 THE COMMON FACTORS ARE 5 & 3 225 5 45 5 9 5 5 3 3 3 10 30 3 5 2

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IDENTIFY COMMON FACTORS 3 5 2 7 5 2 17

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IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 5 & 2 3 5 2 7 5 2 17

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IDENTIFY COMMON FACTORS 7 5 5 3 3 2 5 2 5 7

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IDENTIFY COMMON FACTORS THE COMMON FACTORS ARE 7 & 5 & 5 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 & 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 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 557 253 None 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 225 5 45 5 9 5 5 3 3 3 10 30 3 5 2 Find GCF of 225 & 30 1.Complete Factor Tree for both numbers.

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

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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 1.Complete Factor Tree for both numbers. 2.Identify Common Factors. 3.Multiply Common Factors for GCF 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 45 5 9 5 3 3 5 5 3 25 3 Find LCM of 45 & 25 1.Complete Factor Tree for both numbers. 75

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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 1.Complete Factor Tree for both numbers. 2.Identify Common Factors. 75

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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 1.Complete Factor Tree for both numbers. 2.Identify Common Factors. 3.Multiply Common Factors with ALL OTHER FACTORS LCM = CF’sALL OTHER FACTORS LCM = 53 5 3 = 225 75 OTHER FACTORS

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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 CF’s with ALL OTHER FACTORS

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

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Find LCM of 225, 10 & 66 1.Complete Factor Tree for all numbers. 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

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Find LCM of 225, 10 & 66 1.Complete Factor Tree for all numbers. 2.Identify Common Factors OF ANY 2 #’S. 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

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Find LCM of 225, 10 & 66 1.Complete Factor Tree for all numbers. 2.Identify Common Factors OF ANY 2 #’S. 3.Multiply Common Factors with ALL OTHER FACTORS 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=2535311=4950

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