PRIME FACTORIZATION GCF LCM FACTORING Factoring is the

PRIME FACTORIZATION GCF & LCM

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

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

Factor 225 Prime Factorization

Factor 225 Prime Factorization 1. Put number on top of factor tree.

Factor 225 1. Put number on top of factor tree. 2. Find factors and branch down tree 225 5 45 5 Prime Factorization 9 5 • 3 • 3 = 3 2 • 52

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

HOW TO FIND THE GCF The key to determining the GCF is to identify Common Factors in Both Numbers and Multiplying them together.

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

IDENTIFY COMMON FACTORS 3 • 5 • 2 7 • 5 • 2 • 17

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

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

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

IDENTIFY COMMON FACTORS 7 • 5 • 3 & 2 • 5 • 7 2 • 11 • 5 • 3 • 7 & 13 • 2 • 5 • 2 3 • 5 • 11 • 3 & 2 • 2 • 17 • 7 5 • 7 • 3 & 2 • 5 • 2 • 7 For three numbers common factors must be in all three numbers

IDENTIFY COMMON FACTORS 7 • 5 • 3 & 2 • 5 • 7 2 • 11 • 5 • 3 • 7 & 13 • 2 • 5 • 2 2 • 5 • 3 3 • 5 • 11 • 3 & 2 • 2 • 17 • 7 None 5 • 7 • 3 & 2 • 5 • 2 • 7 For three numbers common factors must be in all three numbers Only 2 is in common

Find GCF of 225 & 30 Finding Greatest Common Factor

Find GCF of 225 & 30 225 5 5 1. Complete Factor Tree for both numbers. 30 45 9 5 • 3 • 3 3 Finding Greatest Common Factor 10 3 • 5 • 2

Find GCF of 225 & 30 225 5 30 45 5 9 5 • 3 • 3 3 10 3 • 5 • 2 THE COMMON FACTORS ARE 5 & 3 Finding Greatest Common Factor 1. Complete Factor Tree for both numbers. 2. Identify Common Factors.

Find GCF of 225 & 30 225 5 30 45 5 9 5 • 3 • 3 3 10 3 • 5 • 2 THE COMMON FACTORS ARE 5 & 3 GCF = 5 • 3 = 15 Finding Greatest Common Factor 1. Complete Factor Tree for both numbers. 2. Identify Common Factors. 3. Multiply Common Factors for GCF

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.

Finding the LCM Least Common Multiple

Find LCM of 45 & 25 Finding Least Common Multiple

Find LCM of 45 & 25 45 5 75 9 5 • 3 25 3 5 • 3 Finding Least Common Multiple 1. Complete Factor Tree for both numbers.

Find LCM of 45 & 25 45 5 75 9 5 • 3 25 3 5 • 3 THE COMMON FACTORS ARE 5 & 3 Finding Least Common Multiple 1. Complete Factor Tree for both numbers. 2. Identify Common Factors.

Find LCM of 45 & 25 45 5 75 9 5 • 3 25 3 5 • 3 Finding Least Common Multiple 1. Complete Factor Tree for both numbers. 2. Identify Common Factors. 3. Multiply Common Factors with ALL OTHER FACTORS THE COMMON FACTORS ARE 5 & 3 LCM = CF’s • ALL OTHER FACTORS LCM = 5 • 3 • 5 • 3 = 225 OTHER FACTORS

Find LCM of 12 & 34 Finding Least Common Multiple 1. Complete Factor Tree for both numbers. 2. Identify Common Factors. 3. Multiply CF’s with ALL OTHER FACTORS

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

Find LCM of 225, 10 & 66 225 10 5 45 5 1. Complete Factor Tree for all numbers. 66 5 • 2 9 5 • 3 • 3 11 Finding the LCM Least Common Multiple (FOR 3 NUMBERS) 6 11 • 3 • 2

Find LCM of 225, 10 & 66 225 10 5 45 5 1. Complete Factor Tree for all numbers. 2. Identify Common Factors OF ANY 2 #’S. 66 5 • 2 9 5 • 3 • 3 11 Finding the LCM Least Common Multiple (FOR 3 NUMBERS) 6 11 • 3 • 2 THE COMMON FACTORS ARE 2, 5 & 3

Find LCM of 225, 10 & 66 225 10 5 45 5 66 5 • 2 9 5 • 3 • 3 11 6 11 • 3 • 2 THE COMMON FACTORS ARE 2, 5 & 3 LCM=2 • 5 • 3 • 11=4950 Finding the LCM Least Common Multiple (FOR 3 NUMBERS) 1. Complete Factor Tree for all numbers. 2. Identify Common Factors OF ANY 2 #’S. 3. Multiply Common Factors with ALL OTHER FACTORS