To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Prime Factorization Worksheets - Page 12

Prime Factorization Worksheets
  • Page 12
 111.  
Using divisibility test, state whether 75 is a prime or a composite number.
a.
Composite
b.
Prime


Solution:

75 is divisible by 5, since it ends with 5.
[Use the divisibility test.]

So, 75 has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

75 is a composite number.


Correct answer : (1)
 112.  
Using divisibility test, find whether 82 is a prime or a composite number.
a.
Prime
b.
Composite


Solution:

The one's digit of 82 is even

Since the one's digit of the number 82 is even, 82 is divisible by 2. It has more than two factors.
[Use the divisibility test.]

A whole number greater than 1 with more than two factors is called a composite number.

82 is a composite number.


Correct answer : (2)
 113.  
Using divisibility test, find whether 54 is a prime or a composite number.
a.
Prime
b.
Composite


Solution:

Since the sum of the digits of the number 54 is divisible by 9, 54 is divisible by 9.
[Use the divisibility test.]

It has more than two factors.

A whole number greater than 1 with more than two factors is called a composite number.

54 is a composite number.


Correct answer : (2)
 114.  
Which of the numbers 18, 13, 11 and 19 is composite?
a.
11
b.
13
c.
18
d.
19


Solution:

A whole number greater than 1 with more than two factors is called a composite number.

The only divisors of 13, 11 and 19 are 1 and the numbers themselves.

Since the sum of the digits of the number 18 is divisible by 3, 18 is divisible by 3. It has more than two factors.
[Use the divisibility test.]

Among the numbers, the number 18 is a composite number.


Correct answer : (3)
 115.  
Write the prime factorization of 256 in exponential form using a factor tree.
a.
25
b.
28
c.
27
d.
26


Solution:


Write the number 256 as a product of two factors and factorize all the composite factors.

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
The prime factorization of 256 is:

256 = 28
[Write in the exponential form.]

The prime factorization of 256 is 28.


Correct answer : (2)
 116.  
Find the prime factorization of 325 using a factor tree.
a.
52 × 131
b.
52 × 31
c.
52 × 132
d.
53 × 131


Solution:


Write the number 325 as a product of two factors and factorize the remaining composite factors.

The prime factors of 325 are: 325 = 5 × 5 × 13

325 = 52 × 131
[Write in the exponential form.]

The prime factorization of 325 is 52 × 131.


Correct answer : (1)
 117.  
Find the prime factorization of 160 in exponential form using a factor tree.
a.
23 × 51
b.
25 × 52
c.
25 × 51
d.
24 × 51


Solution:


Write the number 160 as a product of two factors and factorize the composite factors.

160 = 2 × 2 × 2 × 2 × 2 × 5
The prime factorization of 160 is:

160 = 25 × 51
[Write in the exponential form.]

The prime factorization of 160 is 25 × 51.


Correct answer : (3)
 118.  
Express 18 as difference of two prime numbers.
a.
(29 - 11)
b.
(31 - 13)
c.
(30 - 12)
d.
(28 - 10)


Solution:

A whole number greater than 1 with exactly two factors 1 and itself is called a prime number.

18 can be expressed as a difference of two prime numbers in two ways, which is:29 - 11 = 18, 23 - 5 = 18 .

Among the choices, 18 is expressed as (29 - 11), which is the difference of two prime numbers.


Correct answer : (1)
 119.  
Which number in the set of numbers (2, 5, 9, 3) is a common factor among the prime factors of 4, 10 and 18?
a.
5
b.
2
c.
9
d.
3


Solution:

The prime factors of 4 are: 4 = 2 x 2.

The prime factors of 10 are: 10 = 5 x 2.

The prime factors of 18 are: 18 = 3 x 3 x 2.

In the set of numbers, the number 2 is a common factor among the prime factors of 4, 10 and 18.


Correct answer : (2)
 120.  
Find the product of all the prime factors of 16.
a.
4
b.
16
c.
21
d.
8


Solution:

The product of all the prime factors of any number is the number itself.

The product of all the prime factors of the number 16 is 16.


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.