Factors, Multiples & Prime numbers

FACTO

RS, MULT

IPLE

S &

PRIM

E NUMBERS

GC

F & L

CM

WHAT’S A FACTOR?

A number that can be divided evenly into another number.

Students will often identify multiples instead of factors.

Students often miss a factor when listing them.

Will divide evenly into only some greater numbers.

There are a limited amount of factors for each number.

Usually identified in pairs.

Factor

WHAT’S A MULTIPLE?

A number that can be divided evenly by another number.

Students will often identify factors instead of multiples.

Every number has multiplesThere are an infinite amount of

multiples for each number.Created by pairs of factors.

MultipleMultiplication tables are just lists of multiples.

WHAT’S A PRIME NUMBER?

A number that can be divided only by itself and 1.

Students often think odd numbers are prime numbers. Example: 9

Every number can be divided by a prime number.

Prime numbers are the foundation of all numbers.

Prime Number

Makes All Types of Division Easier!

Long DivisionWriting a number in lowest terms

GCFLCMDistributive Property

Simplify Fractions

Solving RatiosMuch More

Divisibility Rules

WHY USE PRIME NUMBERS?

Just like houses are built from bricks…

Composite numbers are built from prime numbers…

So, we will use the prime numbers:2, 3, 5 and sometimes 7…

To break down composite numbers.

24

12

3

6

÷

2

2

2

13

List all of the factors of 54:

GREATEST COMMON FACTOR

2

1

6

3

18

9

2754

If one number is a factor of the original number, all of its factors are factors of the original number, too!

Ex: A peanut butter sandwich has peanut butter on it. Peanut butter has peanuts. Since peanut butter has peanuts and is on the peanut butter sandwich, the peanut butter sandwich has peanuts, too!

Since 54 has a factor of 6, then the factors of 6 (1, 2, 3, 6) are factors of 54, too.

Since 54 has the factors of 3 and 9, then the product of 3 & 9 (3 x 9 = 27) will create a factor of 54, too!

Using that thinking, what other factor can you find? Enter it into your MathBerry.

6 x 3 = 18; 18 is a factor, too!

What happens when we have to find factors for more than one number AND find the GCF?

What happens, if we miss a factor?

Do you really want to find factors that don’t matter?

Let’s work smarter, not harder!

Use prime numbers:(1)To find only the common factors

(2)To find the correct greatest common factor. (3)Avoid making mistakes.

GREATEST COMMON FACTOR

First, let’s learn how to use the

GCF Gold Digger!

You will need the first four prime numbers: 2, 3, 5 & 7

GREATEST COMMON FACTOR

The numbers you want to factor, go here!

Now… think like a Gold Digger!

Starting with the first prime number (2), can it divide evenly into both of the original numbers?

(Hint: Use your divisibility rules!)

If YES, put it here.

The quotient of 2 goes below each dividend.DIG! Divide by 2 until you cannot divide by 2 anymore!

If NO, move to the next prime number (3) and repeat!

Once the dividends cannot be divided by any prime number, stop.

24

12

2

6

÷

2

3

2

36

18

9

3

GREATEST COMMON FACTOR

2, 3, 5 & 7

Now that all common prime number factors have been found, use

them to ‘build’ the Greatest Common

Factor.

2 x 2 x 3 = 12

24

12

2

6

÷

2

3

2

36

18

9

3

GREATEST COMMON FACTOR

2, 3, 5 & 7

GCF

4 x

x

3

12

12

=

The numbers you want to factor, go here!

Now… think like a Gold Digger!

Starting with the first prime number (2), can it divide evenly into both of the original numbers?

(Hint: Use your divisibility rules!)

If YES, put it here.

The quotient of 2 goes below each dividend.DIG! Divide by 2 until you cannot divide by 2 anymore!

If NO, move to the next prime number (3) and repeat!

Once the dividends cannot be divided by any prime number, stop.

18

9

1

3

÷

3

3

2

90

45

15

5

GREATEST COMMON FACTOR

2, 3, 5 & 7

Now that all common prime number factors have been found, use

them to ‘build’ the Greatest Common

Factor.

2 x 3 x 3 = 18

18

9

1

3

÷

3

3

2

90

45

15

5

GREATEST COMMON FACTOR

2, 3, 5 & 7

GCF

6 x

x

3

18

18

=

The numbers you want to factor, go here!

Now… think like a Gold Digger!

Starting with the first prime number (2), can it divide evenly into both of the original numbers?

(Hint: Use your divisibility rules!)

If YES, put it here.

The quotient of 2 goes below each dividend.DIG! Divide by 2 until you cannot divide by 2 anymore!

If NO, move to the next prime number (3) and repeat!

Once the dividends cannot be divided by any prime number, stop.

50

25

5

÷

5

2

90

45

9

GREATEST COMMON FACTOR

2, 3, 5 & 7

Now that all common prime number factors have been found, use

them to ‘build’ the Greatest Common

Factor.

2 x 5 = 10

50

25

5

÷

5

2

90

45

9

GREATEST COMMON FACTOR

2, 3, 5 & 7

GCF

10

x

10

=

Show your work on your white board and

enter your answer into your MathBerries!

3 x 3 = 9

45

15

5

÷

3

3

99

33

11

NOW, YOU TRY!

2, 3, 5 & 7

GCF

9 x

9=

FACTO

RING S

INGLE

DIGIT

NUMBERS

AD

DI T

I ON

AL

WO

RK

WI T

H S

I NG

LE

NU

MB

ER

F AC

TO

RI N

G

The following slides are not needed for this unit, but provide challenging

work through application of prime numbers to factoring.

Attention to detail is needed.

(1) Find all prime number factors for the number.(2) List 1.

(3) List each factor from the chart once.(4) Multiply each row across.

2 x 25 = 505 x 5 = 25

(5) Multiply as many combinations of the prime number factors from the chart, as you can to find

any remaining composite factors.2 x 5 = 105 x 5 = 25

50

25

5

÷

5

2

FACTORING USING PRIME NUMBERS

1, 10,

5, 2, 50

25,

24

12

6

÷

2

2

FACTORING USING PRIME NUMBERS

1, 3, 4, 2, 24

12,

32

6, 8,

(1) Find all prime number factors for the number.(2) List 1.

(3) List each factor from the chart once.(4) Multiply each row across.

2 x 12 = 242 x 6 = 122 x 3 = 6

(5) Multiply as many combinations of the prime number factors from the chart, as you can to find any

remaining composite factors.2 x 2 = 4 2 x 3 = 6

2 x 2 x 2 = 8 2 x 2 x 3 = 122 x 2 x 2 x 3 = 24

36

18

9

÷

2

2

FACTORING USING PRIME NUMBERS

1, 3, 4, 2,

36

18,

33

6, 9,

3 1

12,

(1) Find all prime number factors for the number.(2) List 1.

(3) List each factor from the chart once.(4) Multiply each row across.

2 x 18 = 362 x 9 = 183 x 3 = 93 x 1 = 3

(5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining

composite factors.2 x 2 = 4 2 x 3 = 62 x 2 x 3 = 12 2 x 3 x 3 = 18

2 x 2 x 2 x 3 = 36

18

9

3

÷

3

2

NOW, YOU TRY!

1, 6, 3, 2, 18

9,

(1) Find all prime number factors for the number.(2) List 1.

(3) List each factor from the chart once.(4) Multiply each row across.

2 x 9 = 183 x 3 = 93 x 1 = 3

(5) Multiply as many combinations of the prime number factors from the chart, as you can to find any

remaining composite factors.2 x 3 = 63 x 3 = 9

2 x 3 x 3 = 18

3 1

(1) Find all prime number factors for the number.(2) List 1.

(3) List each factor from the chart once.(4) Multiply each row across.2 x 45 = 90 3 x 15 = 453 x 5 = 15 5 x 1 = 5

(5) Multiply as many combinations of the prime number factors from the chart, as you can to find any remaining composite factors.

2 x 3 = 6 2 x 5 = 103 x 3 = 9 3 x 5 = 15

2 x 3 x 3 = 18 2 x 3 x 5 = 303 x 3 x 5 = 45 2 x 3 x 3 x 5 = 90

90

45

15

÷

3

2

NOW, YOU TRY!

1, 3, 5, 2, 30,

18,

53

6, 9,

5 1

10,

15,

45,

90