in math •  last year

Yesterday I did a post on times tables which are the key to multiply or divide the numbers. Today there is another application of times tables and which is the Greatest Common Factor also known as gcf. What is Greatest Common Factor or gcf? It is also known as Greatest Common Divisor gcd.

The greatest common factor (gcf) of two or more given numbers is the greatest factor that exactly divides the given numbers.   

How to find the greatest common factor?

To find the gcf of two or more numbers following steps are used:

Method 1:

Find all the factors of the given numbers and then find the common factor which is the greatest. 

For example: Let's find the gcf of 18 and 30. We will write all the factors of 18 and 30 as shown below:

18 = 1, 2, 3, 6, 9, 18

30 = 1, 2, 3, 5, 6, 10, 15, 30

The common factors are 1, 2, 3 and 6. Now we have to pick the greatest common factor which is 6 obviously. Hence the gcf of 18 and 30 is 6.  
 Method 2:    

  • Find all the prime factors of each number. 
  • Multiply the common factors from the above list to find the gcf.

For example; Let's find the gcf of 12 and 18:    

  • Find the prime factors of 12 and 18 as follows:
  • 12 = 2 x 2 x 3
  • 18 = 2 x 3 x 3

 Now the common factors are 2 and 3 . Multiply them as shown below to get the gcf of 12 and 18:

                                                 GCF of 12 and 18 = 2 x 3 = 6 answer    

Use the following lesson and practice sheet to learn how find the prime factors of a number:

Click for pdf version of above worksheet
Remember if there is no common factor found then the gcf is 1. 

Below is a practice sheet on finding gcf of given numbers:

Click for pdf version of above worksheet
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