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

Prime Factorization Worksheets - Page 7

Prime Factorization Worksheets
  • Page 7
 61.  
Using the factor tree, find the cube root of 729.

a.
6
b.
7
c.
8
d.
9


Solution:

From the factor tree, the prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3.

(3 × 3 × 3 × 3 × 3 × 3)1/3 = 3 × 3
[Take the cube root of the factors of 729.]

3 × 3 = 9
[Multiply.]

The cube root of 729 is 9.


Correct answer : (4)
 62.  
Choose the factor tree for 24.

a.
Figure - 1
b.
Figure - 2
c.
Figure - 3
d.
Figure - 1 & Figure - 2


Solution:

The factor tree is used to find a number's prime factors. So, the leaves of a factor tree should be prime numbers.

= 3 × 8
24
[Using prime factorization.]

= 3 × 2 × 4

= 3 × 2 × 2 × 2

So, Figure - 1 is the factor tree of 24.


Correct answer : (1)
 63.  
Find the values of a, b and c in the factor tree.

a.
54, 2, 9
b.
36, 3, 6
c.
36, 3, 15
d.
21, 2, 6


Solution:

From the factor tree, a = 3 × 18 = 54
[Multiply 3 and 18.]

From the factor tree, 18 = b × c

18 = 2 × 9 = 3 × 6
[Express 18 as the product of two numbers.]

The values of a, b and c are 54, 2 and 9.


Correct answer : (1)
 64.  
Which two factor trees model the same number?


a.
Figure - 2 & Figure - 4
b.
Figure - 1 & Figure - 4
c.
Figure - 1 & Figure - 2
d.
Figure - 1 & Figure - 3


Solution:

In Figure - 1, the number in the box at the second level from the top of the tree = 2 × 2 = 4.

The number at the top of the tree = 16 × 4 = 64.

In Figure - 2, the number in the box at the second level of the tree from top = 5 × 3 = 15.

The number at the top of the tree = 5 × 15 = 75.

In Figure - 3, the number in the box at the second level from the top of the tree = 2 × 4 = 8.

The number at the top of the tree = 8 × 8 = 64.

In Figure - 4, the number at the top of the tree = 13 × 4 = 52.

The factor trees in Figure - 1 & Figure - 3 model the same number 64.


Correct answer : (4)
 65.  
Identify the factor trees that model prime factorization of the number.


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


Solution:

In Figure 1, 2 and 3 are prime numbers and 4 is not a prime number.

So, Figure 1 does not model the prime factorization of 24.

In Figure 2, 2 and 13 are prime numbers.

So, Figure 2 models the prime factorization of 52.

In Figure 3, 2 is a prime number and 4 is not a prime number.

So, Figure 3 does not model the prime factorization of 32.

Only Figure 2 models the prime factorization of the number.


Correct answer : (2)
 66.  
Find the cube root of 216 from the factor tree.

a.
18
b.
6
c.
24
d.
12


Solution:

From the factor tree, 216 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33.

The cube root of 216 = 2 × 3 = 6
[Get one 2 out of three 2's and one 3 out of three 3's and multiply.]


Correct answer : (2)
 67.  
Find the square root of 81 from the factor tree.


a.
27
b.
81
c.
9
d.
3


Solution:

From the factor tree, 81 = 3 × 3 × 3 × 3 = 32 × 32.

The square root of 81 = 3 × 3 = 9.
[Get two 3's out of four and multiply.]


Correct answer : (3)
 68.  
Using the factor tree, find the quotient obtained when 216 is divided by 27.


a.
4
b.
3
c.
9
d.
8


Solution:

From the factor tree, 216 = 8 × 27.

The quotient obtained when 216 divided by 27 is 8.


Correct answer : (4)
 69.  
What are the values of a, b and c in the factor tree?

a.
16, 2, 2
b.
16, 2, 4
c.
16, 2, 3
d.
None of the above


Solution:

From the factor tree, a = 2 × 8 = 16
[Multiply 2 and 8.]

From the factor tree, 8 = b × 4.

8 = 2 × 4
[Express 8 as a multiple of 4.]

So, b = 2.

From the factor tree, 4 = c × 2.

4 = 2 × 2
[Express 4 as a multiple of 2.]

So, c = 2.

The values of a, b and c are 16, 2 and 2.


Correct answer : (1)
 70.  
Find the prime factorization of 8 using the factor tree.
a.
2 × 2 × 2
b.
8 × 1
c.
2 × 6
d.
2 × 4


Solution:



Since 2 is a prime number, the prime factorization of 8 = 2 × 2 × 2.


Correct answer : (1)

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