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Worksheets

Prime Factorization

Total questions: 70

Worksheet time: 4hrs 33mins

Name
Class
Date
1.

Find the prime factorization of 18

a)

2 • 9

b)

22 • 3

c)

2 • 32

d)

3 • 6

2.

Find the prime factorization of 60

a)

5 • 12

b)

2 • 32 • 5

c)

22 • 3 • 5

d)

27

3.

Find the prime factorization of 30

a)

22 • 5 • 7

b)

2 • 32

c)

2 • 3 • 7

d)

2 • 3 • 5

4.

Find the prime factorization of 81

a)

22 • 7

b)

23 • 5 • 7

c)

43

d)

34

5.

Find the prime factorization of 108

a)

23 * 32

b)

22 • 33

c)

25 • 3

d)

2 • 3 • 7 • 11

6.

Find the prime factorization of 420

a)

22 • 3 • 5 • 7

b)

77

c)

22 • 3 • 11

d)

23 • 3 • 7

7.

What number has the prime factorization of 23 • 11?

a)

55

b)

66

c)

88

d)

99

8.

What number has the prime factorization of 23 • 32 • 5?

a)

360

b)

720

c)

180

d)

240

9.
Write 28 as a product of its prime factors.
a)
2x2x7
b)
4x7
10.
Write 54 as a product of its prime factors.
a)
2x2x3x3
b)
2x3x3x3
c)
2x3x9
d)
6x9
11.
Write 68 as a product of its prime factors.
a)
2x34
b)
4x17
c)
2x2x17
d)
2x3x17
12.
Which list contains all prime numbers?
a)
2, 3, 5, 7, 11
b)
2, 3, 5, 7, 9
c)
2, 4, 5, 7, 11
d)
2, 3, 5, 7, 12
13.
Write 105 as a product of its prime factors.
a)
3x5x7
b)
15x7 
c)
3x35
d)
2x5x7
14.
Write 92 as a product of its prime factors.
a)
4x23
b)
2x46
c)
2x2x23
d)
2x3x23
15.
Write 64 as a product of its prime factors.
a)
8x8
b)
4x4x4
c)
2x2x2x2x2x2
d)
2x2x4x4
16.
210 written as a product of its prime factors is 2x3x5x7.
a)
True
b)
False
17.
Write 63 as a product of its prime factors. 
a)
2x3x7
b)
3x21
c)
9x7
d)
3x3x7
18.
2 x 2 x 2 is the prime factorization of
a)
6
b)
12
c)
22
d)
8
19.

Use a factor tree to find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

20.

Use a factor tree to find the prime factorization of 32

a)

2x2x2x4

b)

2x2x2x2x2

c)

4x4x2

d)

2x2x2x2x1

21.

Use a factor tree to find the prime factorization of 60

a)

5x3x2x2

b)

7x6x5

c)

5x3x3x2

d)

7x5x4

22.

Use a factor tree to find the prime factorization of 42

a)

4x4x3

b)

6x7

c)

7x3x2

d)

5x4x2

23.

Use a factor tree to find the prime factorization of 64

a)

4x4x4

b)

4x4x2x2

c)

2x2x2x2x2x2

d)

4x4x2x1

24.

Use a factor tree to find the prime factorization of 33

a)

33

b)

11x3

c)

10x3

d)

3x3x3x2

25.
Which is the prime factorization of 12? 
a)
2 x 6
b)
2 + 2 + 2 + 2 + 2 + 2 
c)
22 x 3
d)
1 x 22 x 3
26.

Find the prime factorization of 144

a)

22 x 34

b)

24 x 32

c)

23 x 33

d)

24 x 33

27.

Find the prime factorization of 72

a)

23 x 32

b)

2 x 32 x 4

c)

24 x 33

d)

22 x 62

28.

Find the prime factorization for 80

a)

42 ⋅ 5

b)

24 ⋅ 5

c)

2 ⋅ 2 ⋅ 2

d)

8 ⋅ 5 ⋅ 2

29.

Find the prime factorization of 54.

a)

32 x 6

b)

33 x 2

c)

23 x 3

d)

9 x 6

30.

Find the prime factorization of 24.

a)

23 x 3

b)

22 x 3 x 4

c)

22 x 3

d)

3 x 8

31.

Find the prime factorization of 75.

a)

3 x 52

b)

3 x 5 x 5

c)

32 x 5

d)

5 x 15

32.

Find the prime factorization of 150.

a)

23 x 3 x 5

b)

2 x 52

c)

2 x 3 x 52

d)

52 x 6

33.

Which of the following is NOT prime?

a)

29

b)

23

c)

17

d)

39

34.

Find the prime factorization of 105

a)

7x5x3

b)

11x5x3

c)

7x5x2x1

d)

7x5x3x2

35.

Using a Factor Tree, find the prime factorization of 24.

a)

23 x 3

b)

22 x 3 x 4

c)

22 x 3

d)

3 x 8

36.

Using a Factor Tree, find the prime factorization of 24.

a)

23 x 3

b)

22 x 3 x 4

c)

22 x 3

d)

3 x 8

37.

Find the prime factorization of 18.

a)

2 • 32

b)

2 • 9

c)

22 • 3

d)

3 • 6

38.

Find the prime factorization of 60.

a)

3 • 6

b)

22 • 3 • 5

c)

2 • 32 • 5

d)

27

39.

Find the prime factorization of 30.

a)

22 • 5 • 7

b)

2 • 32

c)

2 • 3 • 7

d)

2 • 3 • 5

40.

Find the prime factorization of 108.

a)

23 * 32

b)

22 • 33

c)

25 • 3

d)

2 • 3 • 7 • 11

41.

What number has the prime factorization of 23 • 11?

a)

55

b)

66

c)

88

d)

99

42.

The prime factors of 70 are?

a)

3 x 5 x 7

b)

5 x 7 x 7

c)

2 x 5 x 7

43.

Find the prime factorization of 56.

a)

2x2x2x7

b)

2x28

c)

3x3x7

44.

Use a factor tree to find the prime factorization of 32

a)

2x2x2x4

b)

2x2x2x2x2

c)

4x4x2

d)

2x2x2x2x1

45.
Use a number tree to find the prime factorization of 60
a)
5x3x2x2
b)
7x6x5
c)
5x3x3x2
d)
7x5x4
46.
Use a number tree to find the prime factorization of 105
a)
7x5x3
b)
11x5x3
c)
7x5x2x1
d)
7x5x3x2
47.
Write 54 as a product of its prime factors.
a)
2x2x3x3
b)
2x3x3x3
c)
2x3x9
d)
6x9
48.
Write 68 as a product of its prime factors.
a)
2x34
b)
4x17
c)
2x2x17
d)
2x3x17
49.

Find the prime factorization of 420

a)

22 • 3 • 5 • 7

b)

77

c)

22 • 3 • 11

d)

23 • 3 • 7

50.

What is the prime factorization of 40 ?

a)

8 x 5

b)

2 x 4 x 5

c)

2 x 2 x 2 x 5

d)

2 x 4 x 8 x 5

51.

What is the divisibility rule for 5?

a)

It is divisible by 2 and 3

b)

The last digit is a five

c)

The last digit is five or zero

d)

The last digit is zero

52.

Which of the following statements is true of this number?

a)

It is divisible by 3 and 9

b)

It is divisible by 2, 3, and 6

c)

It is divisible by 3

d)

It is prime

53.

What is the divisibility rule of 3?

a)

The sum of the digits is a number divisible by 3

b)

The last digit is a 3

c)

The last two digits form a number divisible by 3

d)

The last digit is zero

54.

What is the divisibility rule for 10?

a)

It is divisible by 2 and 3

b)

The last digit is a five

c)

The last digit is five or zero

d)

The last digit is zero

55.

Which of the following statements is true of this number?

a)

It is divisible by 2, 5 and 10

b)

It is divisible by 10

c)

It is divisible by 2, 3, 5, 6, 9, and 10

d)

It is divisible by 3 and 5

56.

What is the divisibility rule of 9?

a)

The sum of the digits is a number divisible by 3

b)

The sum of the digits is a number divisible by 9

c)

The last two digits form a number divisible by 3

d)

The last digit is zero

57.

What is the divisibility rule for 6?

a)

It is divisible by 2 and 3

b)

It is divisible by 3 and 4

c)

It is divisible by 2 and 4

d)

The last digit is zero

58.

Which of the following statements is true of this number?

a)

It is divisible by 2, 3, 4, 6, and 9

b)

It is divisible by 2, 3, 6, and 9

c)

It is divisible by 2, 3, 4, and 6

d)

It is divisible by 2, 4, and 9

59.
Is 525 divisible by 5?
a)
Yes
b)
No
60.
All of these numbers are divisible by 5 except for...
a)
75,395
b)
984,940
c)
222,222,235
d)
8,943,892
61.
Is 816 divisible by 3?
a)
Yes
b)
No
62.

Is 555,509 divisible by 3?

a)

Yes

b)

No

63.
70 can be evenly divided by which number?
a)
5
b)
10
c)
2
d)
All of the above
64.

252 is divisible by 9 because:

a)

The number is divisible by 2 and 3

b)

The sum of the digits can be divided by 9 evenly

c)

The sum of the digits can be divided by 3.

d)

The sum of the digits is even.

65.

Is 19,584 divisible by 9?

a)

Yes

b)

No

66.
Is 64 divisible by 2?
a)
Yes
b)
No
67.

Which number is divisible by 6

a)

1782

b)

1213

c)

536

68.

Which number is divisible by 9

a)

345

b)

8522

c)

98874

69.
Is 81 divisible by 3?
a)
Yes
b)
No
70.
Which of these is divisible by 10?
a)
8105
b)
375
c)
460
d)
52

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