HIGHEST COMMON FACTOR WORKSHEET

1) Find the highest common factor of the numbers 40 and 56 by division method. 

2) Find the highest common factor of the numbers 18, 24 and 30 by factor tree method. 

3) Find the highest common factor of the numbers 36 and 48 by prime factorization method. 

4) Find the highest common factor of the numbers 156 and 124 by division method. 

5) Find the highest common factor of the numbers 16 and 24 by division method. 

6) Find the highest common factor the numbers 84 and 120 by division method. 

7) Find the highest common factor of the numbers 30, 40 and 60 by division method. 

8) Find the highest common factor of the numbers 0.72 and 0.96.

9) Find the highest common factor of the numbers 0.48 and 0.6.

10) Find the highest common factor of the two fractions 3/5 and 7/10.

Detailed Answer Key

1. Answer :

The product of common factors of 40 and 56 is

=  2 x 2 x 2

=  8

So, HCF (40, 56) = 8.

2. Answer :

Find the factors of 18, 24 and 30 by tree method. 

Let us find the factors of 18, 24 and 30 (use of  divisibility test rules will also help).

Factors of 18 ; 

1, 2, 3, 6, 9 and 18.

Factors of 24 : 

1, 2, 3, 4, 6, 8, 12 and 24.

Factors of 30 :

1, 2, 3, 5, 6, 10, 15 and 30.

The factors that are common to all the three given numbers are 1, 2, 3 and 6 of which 6 is the highest.

So, HCF (18, 24, 30) = 6.

Note :

1 is a trivial factor of all numbers.

3. Answer :

Write the prime factors of 36 and 48. 

36  =  2 x 2 x 3 x 3 

48  =  2 x 2 x 2 x 2 x 3

Prime factors that are common to 36 and 48 :

2, 2 and 3

Product of common prime factors :

=  2 x 2 x 3

=  12

So, HCF (36, 48) = 12.

4. Answer :

The product of common factors of 156 and 124 is

=  2 x 2

=  4

So, HCF (156, 124) = 4.

5. Answer :

The product of common factors of 16 and 24 is

=  2 x 2 x 2

=  8

So, HCF (16, 24) = 8.

6. Answer :

The product of common factors of 84 and 120 is

=  2 x 2 x 3

=  12

So, HCF (84, 120) = 12.

7. Answer :

The product of common factors of 30, 40 and 60 is

=  2 x 5

=  10

So, HCF (30, 40, 60) = 10.

8. Answer : 

In the given two numbers 0.72 and 0.96, we find equal number of digits after the decimal point. That is, two digits. 

To get rid of the decimal point, we have to multiply each number by 100.

0.72 x 100  =  72

0.96 x 100  =  96

Find the greatest common factor 72 and 96 using prime factorization method.

Write the prime factors of 72 and 96 as shown below. 

72  =  2 x 2 x 2 x 3 x 3 

96  =  2 x 2 x 2 x 2 x 2 x 3

The prime factors that are common to 72 and 96 are

2, 2, 2 and 3

Product of common prime factors :

=  2 x 2 x 2 x 3

=  24

HCF (72, 96) = 24.

Divide the HCF (24) by 100.

24/100  =  0.24

So, the highest common factor of 0.72 and 0.96 is

0.24

9. Answer : 

In the given two numbers 0.48 and 0.6, we find more number of digits after the decimal point in 0.48. That is, two digits. 

(To get rid of the decimal point, always we have to multiply both the numbers by the same powers of 10)

To get rid of the decimal point, we have to multiply each number by 100.

0.48 x 100  =  48

0.6 x 100  =  60

Find the greatest common factor 48 and 60 using prime factorization method.

Write the prime factors of 48 and 60 as shown below. 

48  =  2 x 2 x 2 x 2 x 3 

60  =  2 x 2 x 3 x 5

The prime factors that are common to 48 and 60 are

2, 2 and 3

Product of common prime factors :

=  2 x 2 x 3

=  12

HCF (48, 60) = 12.

Divide the HCF (12) by 100.

12 / 100  =  0.12

So, the highest common factor of 0.48 and 0.6 is

0.12

10. Answer :

Formula to find the highest common factor (HCF) of fractions :

=  HCF of Numerators / LCM of Denominators

*HCF -----> highest common factor

*LCM -----> least common multiple

HCF of numerators (3, 7)  =  1

LCM of denominators (5, 10)  =  10

Greatest common factor of 3/5 and 7/10 is 

=  HCF (3, 7) / LCM (5, 10)

=  1/10

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