PRIME FACTORIZATIONGCF & 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

30

3 10

3 • 2 • 5

PRODUCT

PRIME FACTORS

Prime Factorization

Factor 225

Prime Factorization

Factor 225

1. Put number on top of factor tree. 225

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

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

THE COMMON FACTORS ARE 5 & 3

225

5 45

5 9

5 • 5 • 3 • 3

3 10

30

3 • 5 • 2

IDENTIFY COMMON FACTORS

3 • 5 • 2 7 • 5 • 2 • 17

IDENTIFY COMMON FACTORS

THE COMMON FACTORS ARE 5 & 2

3 • 5 • 2 7 • 5 • 2 • 17

IDENTIFY COMMON FACTORS

7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7

IDENTIFY COMMON FACTORS

THE COMMON FACTORS ARE 7 & 5 & 5

7 • 5 • 5 • 3 • 3 2 • 5 • 2 • 5 • 7

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

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

5•5•7

2•5•3

None

Only 2 is in common

Finding Greatest Common FactorFind GCF of 225 & 30

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.

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.

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

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.

€

1

6+

1

8=

4

24+

3

24=

7

24

Finding the LCMLeast Common Multiple

Finding Least Common MultipleFind LCM of 45 & 25

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

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

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’s•ALL OTHER FACTORSLCM = 5•3 • 5 • 3 = 225

75

OTHER FACTORS

Finding Least Common MultipleFind LCM of 12 & 34

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 LCMLeast Common Multiple

(FOR 3 NUMBERS)

Find LCM of 225, 10 & 66

1. Complete Factor Tree for all numbers.

Finding the LCMLeast Common Multiple

(FOR 3 NUMBERS)225

5 45

5 9

5 • 5 • 3 • 3

11 6

66

11 • 3 • 2

5 • 2

10

Find LCM of 225, 10 & 66

1. Complete Factor Tree for all numbers.

2. Identify Common Factors OF ANY 2 #’S.

Finding the LCMLeast 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

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 LCMLeast 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=2•5•3•5•3•11=4950