COMMON FACTORS WORKSHEET

Problem 1 : 

(a) List all the factors of 10.

(b) List all the factors of 15.

(c) Write down all the common factors of 10 and 15. 

Problem 2 : 

(a) List all the factors of 12.

(b) List all the factors of 18.

(c) Write down all the common factors of 12 and 18. 

Problem 3 : 

(a) List all the factors of 39.

(b) List all the factors of 65.

(c) Write down all the common factors of 12 and 18. 

Problem 4 : 

(a) List all the factors of 8.

(b) List all the factors of 15.

(c) Write down all the common factors of 8 and 15. And also, verify whether 8 and 15 are co-primes. 

Problem 5 : 

Write the common factors of 9, 36 and 45. 

Problem 6 : 

Find the greatest common factor (GCF) of 14 and 21. 

Problem 7 : 

Find the greatest common factor (GCF) of 72 and 96. 

Problem 8 : 

Find the greatest common factor (GCF) of 100, 125 and 200. 

Detailed Answer Key

Solution (1) :

(a) The factors of 10 are

1, 2, 5 and 10

(b) The factors of 15 are

1, 3, 5 and 15

(c) The common factors of 10 and 15 are 

1 and 5

Solution (2) : 

(a) The factors of 12 are

1, 2, 3, 4, 6 and 12

(b) The factors of 18 are

1, 2, 3, 6 and 18

(c) The common factors of 12 and 18 are 

1, 2, 3 and 6

Solution (3) : 

(a) The factors of 39 are

1, 3, 13 and 39

(b) The factors of 65 are

1, 5, 13 and 65

(c) The common factor of 39 and 65 is 13.

Solution (4) : 

(a) The factors of 8 are

1, 2, 4 and 8

(b) The factors of 15 are

1, 3, 5 and 15

(c) The common factor of 8 and 15 is 1.

Because the common factor of 8 and 15 is 1, 8 and 15 are co-primes are relatively prime. 

Solution (5) :

Factors of 9 :  

1, 2, 3, 9

Factors of 36 :

1, 2, 3, 4, 6, 12, 18, 36

Factors of 45 :

1, 3, 5, 9, 15, 45

the common factors of 9, 36 and 45 are

1 and 3

Solution (6) :

14  =  2 x 7

21  =  3 x 7

Here, 7 is the only common prime factor of 14 and 21.

The smallest power of 7 is just 7. 

Therefore, the GCF of 14 and 21 is 7.

Solution (7) :

72  =  2 x 2 x 2 x 3 x 3  =  2³ x 3²

96  =  2 x 2 x 2 x 2 x 2 x 3  =  2⁴ x 3

Here, 2 and 3 are the common prime factors of 72 and 96.

The smallest power of 2 that appears is 2³ and the smallest power of 3 is just 3. 

Therefore, the GCF of 72 and 96 is 

=  2³ x 3

=  8 x 3

=  24

Solution (8) :

100  =  2 x 2 x 5 x 5  =  2² x 5²

125  =  5 x 5 x 5  =  5³

200  =  2 x 2 x 2 x 5 x 5  =  2³ x 5²

Here, 5 is the only common prime factor of all the three numbers. 

The smallest power of 5 that appears is 5².

Therefore, the GCF of 125 and 200 is 

=  5²

=  25

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