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Prime Factorization Worksheets - Page 5

Prime Factorization Worksheets
  • Page 5
 41.  
List all the prime numbers greater than 20 and less than 30.
a.
23, 31, 29
b.
23 and 27
c.
23 and 29
d.
17 and 19


Solution:

A number that has only two factors, one and itself is called a prime number.

List of prime numbers greater than 20 and less than 30 are 23 and 29.


Correct answer : (3)
 42.  
Identify a number that is a multiple of 15.
a.
384
b.
225
c.
275
d.
366


Solution:

When a number divided by 15 leaves a remainder zero, the number is a multiple of 15.

The numbers 384, 366, and 275 do not leave remainder zero when divided by 15.

The number 225 leaves a remainder zero when divided by 15.

Therefore, 225 is a multiple of 15.


Correct answer : (2)
 43.  
Which of the following is a factor of 121?
a.
14
b.
12
c.
11
d.
13


Solution:

121 = 1 × 11 × 11

So, 11 is one of the factors of 121.


Correct answer : (3)
 44.  
Which of the following is a multiple of 25?
a.
625
b.
112
c.
135
d.
220


Solution:

When a number divided by 25 leaves a remainder zero, the number is a multiple of 25.

The numbers 112, 135, and 220 do not leave remainder zero, when divided by 25.

The number 625 leaves a remainder zero, when divided by 25.

So, 625 is a multiple of 25.


Correct answer : (1)
 45.  
Identify the prime number.
a.
57
b.
9
c.
13
d.
33


Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 9 : 1, 3 and 9
Factors of 33 : 1, 3, 11, and 33
Factors of 57 : 1, 3, 19, and 57
Factors of 13 : 1 and 13

The numbers 9, 33, and 57 have more than 2 factors.

So, the number 13 is a prime number.


Correct answer : (3)
 46.  
Identify a prime number.
a.
107
b.
51
c.
121
d.
93


Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 51 : 1, 3, 17, and 51
Factors of 121 : 1, 11, and 121
Factors of 93 : 1, 3, 31, and 93
Factors of 107 : 1 and 107

The numbers 51, 121, and 93 have more than 2 factors.

So, the number 107 is a prime number.


Correct answer : (1)
 47.  
Identify a composite number.
a.
113
b.
59
c.
35
d.
71


Solution:

A composite number has more than two factors.

Factors of 59 : 1, and 59
Factors of 71 : 1 and 71
Factors of 113 : 1 and 113
Factors of 35 : 1, 5, 7, and 35

The number 35 has more than two factors.

So, the number 35 is a composite number.


Correct answer : (3)
 48.  
Identify a prime number.
a.
121
b.
109
c.
93
d.
39


Solution:

A prime number has exactly two factors, 1 and itself.

Factors of 39: 1, 3, 13, and 39.
Factors of 121 : 1, 11, and 121.
Factors of 93 : 1, 3, 31, and 93.
Factors of 109: 1 and 109.

The numbers 39, 121, and 93 have more than 2 factors.

So, the number 109 is a prime number.


Correct answer : (2)
 49.  
Identify a composite number.
a.
119
b.
31
c.
71
d.
51


Solution:

A composite number has more than two factors.

Factors of 31: 1 and 31
Factors of 71: 1 and 71
Factors of 119: 1 and 119
Factors of 51: 1, 3, 17, and 51

The number 51 has more than two factors.

So, the number 51 is a composite number.


Correct answer : (4)
 50.  
Find all the common factors of 16, 28, and 32.
a.
1, 2, 4, 5, and 10
b.
1, 2, and 4
c.
32, 56 and 64
d.
1, 2, 3 and 4


Solution:

16 = 1 × 16, 2 × 8, 4 × 4
[Write the pairs of numbers with a product of 16.]

The factors of 16 are 1, 2, 4, 8 and 16.

28 = 1 × 28, 2 × 14, 4 × 7
[Write the pairs of numbers with a product of 28.]

The factors of 28 are 1, 2, 4, 7, 14 and 28.

32 = 1 × 32, 2 × 16, 4 × 8
[Write the pairs of numbers with a product of 32.]

The factors of 32 are 1, 2, 4, 8, 16 and 32.

The common factors of 16, 28 and 32 are 1, 2 and 4.


Correct answer : (2)

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