PRIME FACTORIZATION GCF & LCM

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.

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

Prime Factorization Factor 225

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

Prime Factorization Factor 225 Put number on top of factor tree. 225 Find factors and branch down tree 225 5 45 5 9 5 • 5 • 3 • 3 = 32 • 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 30 5 45 3 10 5 9 3 • 5 • 2 5 • 5 • 3 • 3 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 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7

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

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

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

Finding Greatest Common Factor Find GCF of 225 & 30

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

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

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 5 45 3 10 5 9 3 • 5 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 5 & 3 GCF = 5 • 3 = 15

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

Finding Least Common Multiple Find LCM of 45 & 25

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

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

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 25 3 5 9 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

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

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

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 45 5 • 2 11 6 5 9 11 • 3 • 2 5 • 5 • 3 • 3

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 45 5 • 2 11 6 5 9 11 • 3 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 2,5 & 3

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 45 5 • 2 11 6 5 9 11 • 3 • 2 5 • 5 • 3 • 3 THE COMMON FACTORS ARE 2,5 & 3 OTHER FACTORS LCM=2•5•3•5•3•11=4950