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Prime Factorization Worksheets - Page 3

Prime Factorization Worksheets
  • Page 3
 21.  
Identify the composite number.
a.
19
b.
31
c.
23
d.
39


Solution:

A number, which has more than two factors is called a composite number.

39 is a composite number as it has four factors 1, 3, 13 and 39.


Correct answer : (4)
 22.  
Which set of numbers represents all the prime numbers between 1 and 24?
a.
2, 3, 5, 7, 11, 13, 17, 19, and 23
b.
2, 3, 5, 7, 9, 11, 13, 17, 19, and 23
c.
2, 3, 5, 11, 13, 17, 19, and 23
d.
1, 2, 4, 5, 11, 13, 17, 19, and 23


Solution:

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

The numbers with exactly two factors between 1 and 24 are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

2, 3, 5, 7, 11, 13, 17, 19, and 23 represent the set of all prime numbers between 1 and 24.


Correct answer : (1)
 23.  
Which of the following is a pair of relatively prime numbers?
a.
(8, 12)
b.
(6, 12)
c.
(8, 15)
d.
(4, 12)


Solution:

Two numbers are said to be relatively prime if their common factor is only 1.

Common factors of 8 and 12 are 1, 2, 4

Common factors of 6 and 12 are 1, 2, 3, 6

Common factors of 4 and 12 are 1, 2, 4

Common factor of 8 and 15 is only 1.

(8, 15) is a pair of relatively prime numbers.


Correct answer : (3)
 24.  
Choose the pair of relatively prime numbers in the following.
a.
(6, 12)
b.
(7, 14)
c.
(6, 13)
d.
(8, 16)


Solution:

Two numbers are said to be relatively prime if their common factor is only 1.

Common factors of 6 and 12 are 1, 2, 3, 6

Common factors of 7 and 14 are 1, 7

Common factors of 8 and 16 are 1, 2, 4, 8

Common factor of 6 and 13 is only 1.

(6, 13) is a pair of relatively prime numbers.


Correct answer : (3)
 25.  
Which of the following is not a pair of relatively prime numbers?
a.
(6, 11)
b.
(6, 9)
c.
(1, 2)
d.
(7, 8)


Solution:

Two numbers are said to be relatively prime if their common factor is only 1.

Common factor of (1, 2), (7, 8), and (6, 11) is only 1. So, they are relatively prime numbers.

Common factors of (6, 9) are 1, 3, 6.

(6, 9) is not a pair of relatively prime numbers.


Correct answer : (2)
 26.  
Which of the following pairs is a pair of relatively prime numbers between 12 and 16?
a.
(13, 15)
b.
(14, 17)
c.
(13, 17)
d.
(15, 17)


Solution:

Two numbers are said to be relatively prime if their common factor is only 1.

All (13, 17), (14, 17), (15, 17), and (13, 15) are pairs of relatively prime numbers.

But, (13, 17), (14, 17), and (15, 17) do not belong to the range of 12 and 16.

From the choices, (13, 15) is a pair of relatively prime numbers between 12 and 16.


Correct answer : (1)
 27.  
Which of the following is neither prime nor composite number?
a.
2
b.
1
c.
4
d.
3


Solution:

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

A composite number has more than two factors.

2, 3 are prime numbers and 4 is a composite number.

1 is neither prime nor composite number.


Correct answer : (2)
 28.  
Which set of numbers represents all the composite numbers between 10 and 20?
a.
14, 15, 16, and 18
b.
12, 13, 14, 15, 16, and 18
c.
12, 14, 15, 16, and 18
d.
13, 17, and 19


Solution:

A composite number has more than two factors.

The numbers with more than two factors between 10 and 20 are 12, 14, 15, 16, and 18.

12, 14, 15, 16, and 18 represent the set of composite numbers between 10 and 20.


Correct answer : (3)
 29.  
What is the prime factorization of 63?
a.
3 × 7 × 3
b.
7 × 3
c.
3 × 21
d.
3 × 6 × 3


Solution:


The factor tree of 63 is:
[63 = 3 × 21, 21 = 7 × 3]

The circled numbers in the factor tree are the prime factors of 63.

63 = 3 × 7 × 3

So, the prime factorization of 63 is 3 × 7 × 3.


Correct answer : (1)
 30.  
Choose the prime factorization of 242.
a.
11 × 11
b.
2 × 2 × 11
c.
2 × 11
d.
2 × 11 × 11


Solution:


The factor tree of 242 is:
[242 = 2 × 121, 121 = 11 × 11.]

The circled numbers in the factor tree are the prime factors of 242.

242 = 2 × 11 × 11

So, the prime factorization of 242 is 2 × 11 × 11.


Correct answer : (4)

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