How to find Common Factors of Numbers

 Let us understand this concept by an example.

Example: Find the Common Factors and Highest Common Factor (HCF) of 28 and 42.Solution:STEP 1: Write all the factors of 2828 ÷ 1 = 28

28 ÷ 2 = 14

 

28 ÷ 3 is 9 and 1 remainder. So, ignore it.

 

28 ÷ 4 = 7

 

28 ÷ 5 is 5 and 3 remainder. So, ignore it. 

 

28 ÷ 6 is 4 and 4 remainder. So, ignore it.

 

28 ÷ 7 = 4

Now the numbers started repeating, 4 and 7. So, stop.Thus, all the factors of 28 are: 1, 2, 4, 7, 14, 28  STEP 2: Write all the factors of 42.42 ÷ 1 = 42

42 ÷ 2 = 21

 

42 ÷ 3 = 14

42 ÷ 4 is 10 and 2 remainder. So, ignore it.

 

42 ÷ 5 is 8 and 2 remainder. So, ignore it. 

 

42 ÷ 6 = 7

 

42 ÷ 7 = 6

Now the numbers started repeating, 6 and 7. So, stop.Thus, all the factors of 42 are:1, 2, 3, 6, 7, 14, 21, 42 STEP 3: The numbers that are occurring in all the factors of both 28 and 42 are COMMON FACTORS of 28 and 42.  Thus, common factors of 28 and 42 are:1, 2, 7, 14 STEP 4: Find Highest Common Factor (HCF) of 28 and 42The biggest number among all the common factors of the given numbers is known as the Highest Common Factor or HCF of given numbers. Thus, Highest Common Factor or HCF of 28 and 42 is 14. RELATED POST:

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