Name _____________________

Prime Factoring
When a number written as the product of prime factors, it is called the prime factorization of a number.
48 = 3 * 2 * 2 * 2 * 2 = 3 * 24
To make finding the prime factors easy, you need to be a master of “The Factor Facts” and Divisibility Rules for 2,
3, 5, 7 and 11. This workbook will review those skills before showing you the strategies for finding prime factors.
There are 2 attack strategies for quickly and easily finding the prime factors of a given number.
1. Easy Primes
2. Ladder

Factor Facts
There are 32 numbers that are supposed to be quick and easy to recognize the factors of. Math6.org calls these
numbers, “Factor Facts” and offers matching exercises and drills to help you learn them quickly and easily.
12 18 25 32 42 50 63 80
14 20 27 35 45 54 64 81
15 21 28 36 48 56 70 90
16 24 30 40 49 60 72 100

Easy Factors
Often called the tree method, easy primes involves learning to think of an easy factor and write it as the product of its
prime factors. Students will think 6 and write 2*3. So when they are thinking 6*8, they write 3*2 *2*2*2. This
process isn’t difficult, but it does take practice to make it so easy that it’s second nature.
4=2*2 6=3*2 8=2*2*2 9=3*3 10 = 5 * 2
Take a look at the “Factor Facts” and notice that all of them are made out factors that can be easily primed.
28 is 7 * 4 = 7 * 2 * 2; 56 is 7 * 8 = 7 * 2 * 2 * 2; 90 is 9 * 10 = 3 * 3 * 5 * 2

Ladders
When you don’t know the “easy factors” of a number, 17
you use the divisibility rules for 2, 3, 5, 7, and 11 to begin
3 51
breaking a number down. Using the divisibility rules and
2 102
short division, you can quickly find all of the prime
2 204
factors of any number.

204 = 17 * 3 * 2 * 2

© 2009 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non-profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”.
The “Factor Facts”
Models
Lesson Box 4•3 12 9 • 6 54
The following numbers are numbers that you should
7•2 14 6•5 30 8 • 7 56
be able to look at and instantly know the factors of.
5•3 15 8•4 32 10 • 6 60
12 25 42 63
14 27 45 64 4•4 16 7•5 35 9 • 7 63
15 28 48 70
16 30 49 72 9•2 18 6•6 36 8 • 8 64
18 32 50 80
20 35 54 81 5•4 20 8•5 40 10 • 7 70
21 36 56 90
24 40 60 100 7•3 21 7•6 42 9 • 8 72
If any of these multiplication facts are still giving you 6•4 24 9•5 45 10 • 8 80
pause and stumbles, please make flash cards, study
“Factor Facts” @ Math6.org, or copy them 10 times 5•5 25 8•6 48 9 • 9 81
each until you are able to instantly declare the factors
for these numbers. 9•3 27 9•5 49 10 • 9 90

7•4 28 10 • 5 50 10 • 10 100

I want you to be much faster and make this skill even easier. I don’t think you need to use the multiplication sign
between the factors the way that I did. As you complete the drill on this page and the drills on the next, you may drop
the multiplication sign and remember that multiplication is commutative – order doesn’t matter! 120 = 12 • 10; you
may write 12 10 on your paper and leave the multiplication sign out.

________ 42 ________ 40 ________ 18 ________ 70

________ 60 ________ 24 ________ 28 ________ 35

________ 54 ________ 64 ________ 100 ________ 42

________ 56 ________ 20 ________ 63 ________ 64

________ 30 ________ 25 ________ 50 ________ 48

________ 21 ________ 45 ________ 12 ________ 15

________ 70 ________ 35 ________ 16 ________ 60

________ 27 ________ 80 ________ 72 ________ 72

________ 49 ________ 81 ________ 14 ________ 56

________ 48 ________ 90 ________ 36 ________ 28

________ 32 ________ 15 ________ 90 ________ 81

[use Key 1 to check your answers]

Factor Facts Drills
Use one drill each day as a warm-up before completing the assignments for the next 3 sections of the workbook.

[Key 3] [Key 4] [Key 5] [Key 6]

________ 70 ________ 64 ________ 90 ________ 14

________ 72 ________ 70 ________ 60 ________ 32

________ 48 ________ 72 ________ 50 ________ 25

________ 45 ________ 12 ________ 54 ________ 56

________ 25 ________ 40 ________ 49 ________ 90

________ 14 ________ 15 ________ 20 ________ 21

________ 54 ________ 45 ________ 12 ________ 45

________ 15 ________ 48 ________ 80 ________ 16

________ 27 ________ 42 ________ 16 ________ 20

________ 60 ________ 24 ________ 63 ________ 28

________ 81 ________ 56 ________ 70 ________ 24

________ 100 ________ 60 ________ 40 ________ 60

________ 64 ________ 32 ________ 35 ________ 54

________ 40 ________ 18 ________ 15 ________ 72

________ 24 ________ 30 ________ 72 ________ 48

________ 56 ________ 49 ________ 27 ________ 70

________ 16 ________ 25 ________ 28 ________ 35

________ 32 ________ 27 ________ 36 ________ 18

________ 20 ________ 80 ________ 32 ________ 40

________ 36 ________ 90 ________ 14 ________ 36

________ 63 ________ 14 ________ 45 ________ 64

________ 42 ________ 28 ________ 48 ________ 42

________ 12 ________ 16 ________ 24 ________ 15

________ 18 ________ 50 ________ 18 ________ 63

________ 49 ________ 20 ________ 64 ________ 81

The “Easy Primes”
Models
Lesson Box

We need to learn to think of a few numbers as the

product of their primes. The easy primes are 4, 6, 8,
9, and 10! 2 = 2
3 = 3
4=2•2
2•2 = 4
6=3•2
8=2•2•2 5 = 5

9=3•3 3•2 = 6

10 = 5 • 2 7 = 7
2•2•2 = 8
When you get good at thinking “10” and writing 5 •
2, the rest of the prime factoring skill will be much 3•3 = 9
easier. Use the drills on this page and/or practice
5•2 = 10
“Easy Primes” @ Math6.org!

I want you to be much faster and make this skill even easier. I don’t think you need to use the multiplication sign
between the factors the way that I did. As you complete the drill on this page, you may drop the multiplication sign
and remember that multiplication is commutative – order doesn’t matter! 6 = 3 • 2; you may write 3 2 on your paper
and leave the multiplication sign out.

_____________ = 5 _____________ = 10 _____________ = 2 _____________ = 3

_____________ = 8 _____________ = 4 _____________ = 4 _____________ = 9

_____________ = 10 _____________ = 3 _____________ = 9 _____________ = 4

_____________ = 4 _____________ = 2 _____________ = 3 _____________ = 5

_____________ = 9 _____________ = 8 _____________ = 7 _____________ = 6

_____________ = 2 _____________ = 6 _____________ = 6 _____________ = 8

_____________ = 3 _____________ = 5 _____________ = 5 _____________ = 4

_____________ = 7 _____________ = 10 _____________ = 2 _____________ = 2

_____________ = 6 _____________ = 5 _____________ = 8 _____________ = 7

_____________ = 7 _____________ = 8 _____________ = 10 _____________ = 10

_____________ = 9 _____________ = 6 _____________ = 7 _____________ = 9

[use Key 7 to check your answers]

The “Easy Factors”
Models
Lesson Box

Now that we know the “Easy Primes”, we put it

together with the “Factor Facts” and easily factor
these numbers! When you see a “Factor Fact” you 7•5 = 35
will know the prime factorization!
3•3•7 = 63

40 = 8 • 5 = 2 • 2 • 2 • 5 5•3 = 15
42 = 7 • 6 = 7 • 3 • 2 5•2•3•3 = 90
63 = 9 • 7 = 3 • 3 • 7 = 16
2•2•2•2
72 = 9 • 8 = 3 • 3 • 2 • 2 • 2
7•2 = 14

Think of the factors and write those factors as easy 3•2•2•2 = 24

primes. You will quickly and easily be able to factor
most of the fractions that you will soon face! Use the
drills on this page and/or practice “Easy Factors” @
Math6.org!

I want you to be much faster and make this skill even easier. I don’t think you need to use the multiplication sign
between the factors the way that I did. As you complete the drills on this page and the next, you may drop the
multiplication sign and remember that multiplication is commutative – order doesn’t matter! 6 = 3 • 2; you may
write 3 2 on your paper and leave the multiplication sign out.

__________________ = 30 __________________ = 36 __________________ = 18

__________________ = 56 __________________ = 21 __________________ = 35

__________________ = 48 __________________ = 25 __________________ = 40

__________________ = 24 __________________ = 63 __________________ = 42

__________________ = 16 __________________ = 81 __________________ = 54

__________________ = 45 __________________ = 70 __________________ = 80

__________________ = 15 __________________ = 32 __________________ = 12

__________________ = 14 __________________ = 50 __________________ = 64

__________________ = 60 __________________ = 90 __________________ = 100

__________________ = 72 __________________ = 20 __________________ = 49

__________________ = 28 __________________ = 27 __________________ = 24

[use Key 8 to check your answers]

Easy Factor Drills
Use one drill each day as a warm-up before completing the assignments for the next 3 sections of the workbook.

[Key 9] [Key 10] [Key 11]

__________________ = 15 __________________ = 40 __________________ = 100

__________________ = 35 __________________ = 80 __________________ = 25

__________________ = 54 __________________ = 24 __________________ = 35

__________________ = 16 __________________ = 14 __________________ = 36

__________________ = 36 __________________ = 81 __________________ = 81

__________________ = 49 __________________ = 12 __________________ = 80

__________________ = 12 __________________ = 30 __________________ = 21

__________________ = 24 __________________ = 28 __________________ = 56

__________________ = 81 __________________ = 42 __________________ = 70

__________________ = 32 __________________ = 60 __________________ = 64

__________________ = 72 __________________ = 27 __________________ = 24

__________________ = 45 __________________ = 64 __________________ = 27

__________________ = 100 __________________ = 100 __________________ = 30

__________________ = 27 __________________ = 25 __________________ = 50

__________________ = 20 __________________ = 15 __________________ = 16

__________________ = 60 __________________ = 21 __________________ = 60

__________________ = 42 __________________ = 90 __________________ = 28

__________________ = 30 __________________ = 50 __________________ = 49

__________________ = 28 __________________ = 16 __________________ = 14

__________________ = 70 __________________ = 20 __________________ = 90

__________________ = 14 __________________ = 70 __________________ = 15

__________________ = 50 __________________ = 72 __________________ = 45

__________________ = 48 __________________ = 45 __________________ = 20

__________________ = 56 __________________ = 36 __________________ = 12

__________________ = 21 __________________ = 48 __________________ = 42

Factor Ladders

Lesson Box Models

When a the prime factorization of a number is not

easily known using “Factor Facts”, you apply the
divisibility rules for 2, 3, 5, 7, and 11 to find a 113 053
divisor. Use short division to build a “Factor 2 226 3 159
Ladder”.

226 = 113 • 2 159 = 53 • 3

1. Check for divisibility by 2, 3, 5, 7, and/or 11.
2. Use short division to find the quotient.
023 023
3. Repeat steps 1 and 2 on the quotient.
2 046 7 161
Continue until the quotient is a prime number. 5 230 2 322

230 = 23 • 5 • 2 322 = 23 • 7 • 2

Use factor ladders to find the prime factorization of each of these numbers. Write the prime factorization on the line
and check your work. Remember that multiplication is commutative so the order of your answers will not matter.

__________________ = 129 __________________ = 74 __________________ = 127

__________________ = 143 __________________ = 133 __________________ = 84

__________________ = 147 __________________ = 96 __________________ = 118

__________________ = 86 __________________ = 171 __________________ = 166

__________________ = 58 __________________ = 51 __________________ = 122

__________________ = 164 __________________ = 156 __________________ = 56

__________________ = 102 __________________ = 126 __________________ = 34

__________________ = 69 __________________ = 152 __________________ = 132

__________________ = 144 __________________ = 180 __________________ = 38

__________________ = 148 __________________ = 159 __________________ = 168

__________________ = 26 __________________ = 177 __________________ = 172

__________________ = 170 __________________ = 93 __________________ = 46

[use Key 12 to check your answers]

Find the Prime Factorization of each of the numbers below. You should use exponents to make writing and checking your work
easier.

Drill A Drill B Drill C

__________________ = 24 __________________ = 17 __________________ = 8

__________________ = 25 __________________ = 18 __________________ = 12

__________________ = 32 __________________ = 20 __________________ = 16

__________________ = 40 __________________ = 21 __________________ = 22

__________________ = 42 __________________ = 44 __________________ = 30

__________________ = 51 __________________ = 49 __________________ = 34

__________________ = 78 __________________ = 50 __________________ = 45

__________________ = 80 __________________ = 58 __________________ = 48

__________________ = 81 __________________ = 63 __________________ = 64

__________________ = 82 __________________ = 72 __________________ = 66

__________________ = 84 __________________ = 87 __________________ = 76

__________________ = 90 __________________ = 95 __________________ = 88

__________________ = 91 __________________ = 98 __________________ = 100

__________________ = 94 __________________ = 220 __________________ = 102

__________________ = 210 __________________ = 225 __________________ = 350

__________________ = 500 __________________ = 400 __________________ = 474

Several of these problems have more than one possible answer. Make sure you want your answer is actually wrong
before you mark it wrong. Also, remember that multiplication is commutative so the order you chose doesn’t matter!
To be much faster, make use the easiest factors the way that I did. Multiplication is commutative – order doesn’t
matter! 120 12 • 10; you may write 12 10 on your paper[Key
and leave
1] the multiplication sign out.

7•6 8 • 5 or 10 • 4 9 • 2 or 6 • 3 10 • 7

10 • 6 8 • 3 or 6 • 4 7•4 7•5

6 • 6 or 9 • 4 8•8 10 • 10 7•6

8•7 5 • 4 or 10 • 2 9•3 8•8

6•5 5•5 10 • 5 8•6

7•3 9•5 4 • 3 or 6 • 2 5•3

10 • 7 7•5 4 • 4 or 8 • 2 10 • 6

9•3 10 • 8 9•8 9•8

7•7 9•9 7•2 8•7

8•6 10 • 9 6 • 6 or 9 • 4 7•4

8•4 5•3 10 • 9 9•9

I Remember that multiplication is commutative – order doesn’t matter! I don’t think you need to use the
multiplication sign between the factors the way that I did. As you complete the drill on this page, you may drop the
multiplication sign and remember that multiplication is commutative – order doesn’t matter! 6 3 • 2; you may write 3
[Key 7]
2 on your paper and leave the multiplication sign out.

5 5•2 2 3

2•2•2 2•2 2•2 3•3

5•2 3 3•3 2•2

2•2 2 3 5

3•3 2•2•2 7 3•2

2 3•2 3•2 2•2•2

3 5 5 2•2

7 5•2 2 2

3•2 5 2•2•2 7

7 2•2•2 5•2 5•2

3•3 3•2 7 3•3

Factor Facts Drills
Use one drill each day as a warm-up before completing the assignments for the next 3 sections of the workbook.

[Key 3] [Key 4] [Key 5] [Key 6]

7•7 8•8 10 • 9 7•2

9•8 10 • 7 10 • 6 8•4

8•6 9•8 10 • 5 5•5

9•5 4 • 3 or 6 • 2 9•4 8•7

5•5 8 • 5 or 10 • 4 7•7 10 • 9

7•2 5•3 5 • 4 or 10 • 2 7•3

8•7 9•5 4 • 3 or 6 • 2 9•5

5•3 8•6 10 • 8 6 • 3 or 8 • 2

9•3 7•6 4 • 4 or 8 • 2 5 • 4 or 10 • 2

10 • 6 6 • 4 or 8 • 3 9•7 7•4

9•9 8•7 10 • 7 6 • 4 or 8 • 3

10 • 10 10 • 6 8 • 5 or 10 • 4 10 • 6

8•8 8•4 7•5 9•6

8 • 5 or 10 • 4 6 • 3 or 9 • 2 5•3 9•8

6 • 4 or 8 • 3 6 • 5 or 10 • 3 9•8 8•6

8•7 7•7 9•3 10 • 7

4 • 4 or 8 • 2 5•5 7•4 7•5

8•4 9•3 6 • 6 or 9 • 4 6 • 3 or 9 • 2

5 • 4 or 10 • 2 10 • 8 8•4 8 • 5 or 10 • 4

6 • 6 or 9 • 4 10 • 9 7•2 6 • 6 or 9 • 4

9•7 7•2 9•5 8•8

7•6 7•4 8•6 7•6

4 • 3 or 6 • 2 6 • 3 or 8 • 2 6 • 4 or 8 • 3 5•3

6 • 3 or 8 • 2 10 • 5 6 • 3 or 9 • 2 9•7

7•7 5 • 4 or 10 • 2 8•8 9•9

 Remember that multiplication is commutative – order doesn’t matter! I don’t think you need to use the multiplication
sign between the factors the way that I did. As you complete the drills on this page and the next, you may drop the
multiplication sign and remember that multiplication is[Key
commutative
8] – order doesn’t matter! 6 = 3 • 2; you may
write 3 2 on your paper and leave the multiplication sign out..

3•2•5 3•2•3•2 3•3•2

2•2•2•7 7•3 7•5

2•2•2•3•2 5•5 2•2•2•5

3•2•2•2 3•3•7 7•3•2

2•2•2•2 3•3•3•3 3•3•3•2

3•3•5 5•2•7 5•2•2•2•2

5•3 2•2•2•2•2 2•2•3

7•2 5•2•5 2•2•2•2•2•2

5•2•3•2 5•2•3•3 5•2•5•2

3•3•2•2•2 5•2•2 7•7

7•2•2 3•3•3 3•2•2•2

Use factor ladders to find the prime factorization of each of these numbers. Write the prime factorization on the line
and check your work. Remember that multiplication is commutative so the order of your answers will not matter.

43 • 3 37 • 2 127 • 1

13 • 11 19 • 7 7•3•2•2

7•7•3 3•2•2•2•2•2 59 • 2

43 • 2 19 • 3 • 3 83 • 3

29 • 2 17 • 3 61 • 2

41 • 2 • 2 13 • 3 • 2 • 2 7•2•2•2

17 • 3 • 2 7•3•3•2 17 • 2

23 • 3 19 • 2 • 2 • 2 11 • 3 • 2 • 2

3•3•2•2•2•2 5•3•3•2•2 19 • 2

37 • 2 • 2 53 • 3 7•3•2•2•2

13 • 2 59 • 3 43 • 2 • 2

17 • 5 • 2 31 • 3 23 • 2

[Key 12]
Easy Factor Drills
Use one drill each day as a warm-up before completing the assignments for the next 3 sections of the workbook.

[Key 9] [Key 10] [Key 11]

5•3 2•2•2•5 5•2•5•2

7•5 5•2•2•2•2 5•5

3•3•3•2 3•2•2•2 7•5

2•2•2•2 7•2 3•2•3•2

3•2•3•2 3•3•3•3 3•3•3•3

7•7 2•2•3 5•2•2•2•2

2•2•3 3•2•5 7•3

3•2•2•2 7•2•2 2•2•2•7

3•3•3•3 7•3•2 5•2•7

2•2•2•2•2 5•2•3•2 2•2•2•2•2•2

3•3•2•2•2 3•3•3 3•2•2•2

3•3•5 2•2•2•2•2•2 3•3•3

5•2•5•2 5•2•5•2 3•2•5

3•3•3 5•5 5•2•5

5•2•2 5•3 2•2•2•2

5•2•3•2 7•3 5•2•3•2

7•3•2 5•2•3•3 7•2•2

3•2•5 5•2•5 7•7

7•2•2 2•2•2•2 7•2

5•2•7 5•2•2 5•2•3•3

7•2 5•2•7 5•3

5•2•5 3•3•2•2•2 3•3•5

2•2•2•3•2 3•3•5 5•2•2

2•2•2•7 3•2•3•2 2•2•3

7•3 2•2•2•3•2 7•3•2

Find the Prime Factorization of each of the numbers below. You should use exponents to make writing and checking your work
easier.

Drill A Drill B Drill C

3 • 23 17 • 1 23

52 32 • 2 3 • 22

25 5 • 22 24

5 • 23 7•3 11 • 2

7•3•2 11 • 22 5•3•2

17 • 3 72 17 • 2

13 • 3 • 2 52 • 2 5 • 33

5 • 24 29 • 2 3 • 24

34 7 • 32 26

41 • 2 32 • 23 11 • 3 • 2

7 • 3 • 22 29 • 3 19 • 22

5 • 32 • 2 19 • 5 11 • 23

91 • 1 72 • 2 52 • 2 2

47 • 2 11 • 5 • 22 17 • 3 • 2

7•5•3•2 52 • 32 7 • 52 • 2

53 • 2 2 52 • 24 79 • 3 • 2