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Prime Factorization Worksheets - Page 8

Prime Factorization Worksheets
  • Page 8
 71.  
Which of the figures represent(s) the factor tree for 120?

a.
figure 1
b.
figure 2
c.
figure 3
d.
figures 1 & 2


Solution:

= 3 × 40
120
[Write 120 as a product of 3 and 40.]

= 3 × 2 × 20
[Write 40 as a product of 2 and 20.]

= 3 × 2 × 2 × 10
[Write 20 as a product of 2 and 10.]

= 3 × 2 × 2 × 2 × 5
[Write 10 as a product of 2 and 5.]

So, figure 3 represents the factor tree for 120.


Correct answer : (3)
 72.  
Find the cube root of 64 from the factor tree.

a.
8
b.
4
c.
6
d.
2


Solution:

From the factor tree, we can write 64 as 2 × 2 × 2 × 2 × 2 × 2.

(2 × 2 × 2) × (2 × 2 × 2)
[Write the product of three 2's as one group.]

2 × 2 = 4
[Select one 2 from each group and multiply.]

The cube root of 64 is 4.


Correct answer : (2)
 73.  
Using divisibility tests, state whether 50 is a prime or a composite number.
a.
Composite
b.
Prime


Solution:

The one's digit of 50 is 0.

A number is divisible by 2, if its one's digit is even and a number is divisible by 5 and 10, if its one's digit is 0.

50 is divisible by 2, 5 and 10.

A number that has factors other than 1 and itself is called a composite number.

50 is a composite number.


Correct answer : (1)
 74.  
Which of the numbers 3, 4, 12 or 15 has a prime factor greater than 3?
a.
3
b.
15
c.
4
d.
12


Solution:

3 = 1 × 3
[Write the prime factorization of 3.]

4 = 2 × 2
[Write the prime factorization of 4.]

12 = 2 × 2 × 3
[Write the prime factorization of 12.]

15 = 3 × 5
[Write the prime factorization of 15.]

5 is a prime and greater than 3.

Only 15 has the prime factor greater than 3.


Correct answer : (2)
 75.  
Is 15 a prime or a composite number?
a.
Composite
b.
Prime
c.
Even prime
d.
Neither prime nor composite


Solution:

To find whether 15 is a prime or composite, draw the rectangles from exactly 15 squares.


The following graph shows that two rectangles of dimensions 3 × 5 and 15 × 1 can be drawn from 15 squares.

The dimensions of the rectangle show that the factors of 15 are 1, 3, 5, and 15.

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

So, 15 is a composite number.


Correct answer : (1)
 76.  
Write the prime factorization of 3 × 2 × 3 × 7 using exponents.
a.
32 × 22 × 71
b.
31 × 22 × 71
c.
32 × 21 × 71
d.
31 × 21 × 71


Solution:

There are two 3's, one 2 and one 7 in the prime factorization.

3 × 2 × 3 × 7 = 32 × 21 × 71
[Factors in their exponential form.]

The prime factorization of 3 × 2 × 3 × 7 using exponents is 32 × 21 × 71


Correct answer : (3)
 77.  
Write the prime factorization of 5 × 2 × 2 using exponents.
a.
51 × 22
b.
52 × 23
c.
52 × 21
d.
51 × 21


Solution:

5 × 2 × 2
[Original expression.]

The prime factorization has one 5 and two 2's.

= 51 × 22
[Factors in their exponential form.]

The prime factorization of 5 × 2 × 2 using exponents is 51 × 22.


Correct answer : (1)
 78.  
Find whether 47 is a prime or a composite number.
a.
Prime
b.
Composite


Solution:

The only divisors of 47 are 1 and 47.

If a number has exactly two factors, 1 and itself, then the number is called a prime number.

47 is a prime number.


Correct answer : (1)
 79.  
Write the prime factorization of 4 × 6 × 6 × 8 × 8 by using exponents.
a.
41 × 63 × 82
b.
41 × 62 × 82
c.
42 × 62 × 82
d.
41 × 62 × 83


Solution:

4 × 6 × 6 × 8 × 8
[Original expression.]

There are one 4, two 6's and two 8's in the prime factorization.

= 41 × 62 × 82
[Factors in their exponential form.]

The prime factorization of 4 × 6 × 6 × 8 × 8 using exponents is 41 × 62 × 82.


Correct answer : (2)
 80.  
Write the prime factorization of 7 × 7 × 7 × 5 × 5 × 5 × 3 × 3 using exponents.
a.
73 × 52 × 32
b.
73 × 53 × 33
c.
73 × 53 × 32
d.
72 × 53 × 32


Solution:

7 × 7 × 7 × 5 × 5 × 5 × 3 × 3
[Original expression.]

There are three 7's, three 5's and two 3's in the prime factorization.

= 73 × 53 × 32
[Write in exponential form.]


Correct answer : (3)

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