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Prime Factorization Worksheets - Page 6

Prime Factorization Worksheets
  • Page 6
 51.  
Identify the prime number.
a.
57
b.
9
c.
13
d.
33


Answer: (c)


Correct answer : (3)
 52.  
Which of the following is the prime factorization of 54?
a.
3 × 2 × 8
b.
2 × 2 × 11
c.
3 × 2 × 3 × 3
d.
3 × 2 × 9


Answer: (c)


Correct answer : (3)
 53.  
Which of the following represents 8 × 8?
a.
28
b.
83
c.
8(2)
d.
82


Answer: (d)


Correct answer : (4)
 54.  
What is the prime factorization of 768?
a.
27 × 31
b.
28 × 31
c.
22 × 53
d.
23 × 31 × 54


Answer: (b)


Correct answer : (2)
 55.  
Find the missing number in the factor tree.


a.
5
b.
4
c.
3
d.
2


Solution:

27 = 3 × 9
[Express 27 as a multiple of 9.]

The missing number in the factor tree is 3.


Correct answer : (3)
 56.  
A rectangle can be formed in two different ways using exactly 18 squares as shown in the figure. Find the factors of 18 excluding 1 and itself.


a.
5, 6 and 9
b.
2, 3, 6 and 9
c.
1, 3, 6 and 18
d.
None of the above


Solution:

The dimensions of the two rectangles are 2 × 9 and 3 × 6.

So, the factors of 18 are 2, 3, 6 and 9.


Correct answer : (2)
 57.  
Find the square root of 144.
a.
14
b.
22
c.
24
d.
12


Solution:


Draw the factor tree for 144 as shown in the figure.

From the factor tree, we can write 144 as 2 × 2 × 3 × 3 × 2 × 2 = 24 × 32.

The square root of 144 is 2 × 2 × 3 = 12.
[Take two 2's and one 3 out of the four 2's and two 3's and multiply.]


Correct answer : (4)
 58.  
Using the factor tree, find the prime factors of 760.


a.
4, 5, 5 and 19
b.
2, 2, 2, 5 and 19
c.
2, 3, 5, 5 and 19
d.
2, 10, 5 and 19


Solution:

From the factor tree, 2, 5 and 19 are the prime numbers.

So, the prime factorization of 760 = 2 × 2 × 2 × 5 × 19.


Correct answer : (2)
 59.  
Select a model for representing the factor tree for 360.

a.
Figure 3
b.
Figure 1
c.
Figure 4
d.
Figure 1 and Figure 2


Solution:

5 x 2 x 2 x 2 x 3 x 3 = 360
[Select the prime factors from figure 1 and multiply.]

2 x 5 x 2 x 2 x 3 x 3 = 360
[Select the prime factors from figure 2 and multiply.]

3 x 3 x 2 x 2 = 36
[Select the prime factors from figure 3 and multiply.]

3 x 3 x 7 x 2 x 2 = 252
[Select the prime factors from figure 4 and multiply.]

In both figure 1 and figure 2, the product of the prime numbers is 360.

So, figure 1 and figure 2 are the models that represent the factor tree for 360.


Correct answer : (4)
 60.  
Find the G.C.F of 24 and 32, using the factor trees.

a.
3
b.
4
c.
6
d.
8


Solution:

From the factor trees, the prime factorization of 24 is 2 x 2 x 2 x 3 and 32 is 2 x 2 x 2 x 2 x 2.

Both 24 and 32 have the common factors 2 x 2 x 2.

The product of the common factors is 2 x 2 x 2 = 8.

The G.C.F of 24 and 32 is 8.


Correct answer : (4)

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