Highest Common Factor


 
 
Concept Explanation
 

Highest Common Factor

The highest number that divides exactly into two or more numbers.It is the "greatest" thing for simplifying fractions.

To find the highest common factor of two (or more) numbers, make prime factors of the numbers and identify the common prime factors. Then the highest common factor is the product of the common prime factors.

Illustration 1:  Find HCF of  8 and 12 .

Solution: Factors of 8 : 1,2,4,8

Factors of 12 : 1,2,3,4,6,12

So, the common factors of 8 and 12 are:1,2,4

HCF = 4

Illustration 2:  Find HCF of  10 and 12 .

Solution: Factors of 10 : 1,2,5,10

Factors of 12 : 1,2,3,4,6,12

So, the common factors of 10 and 12 are:1,2

HCF = 2

Illustration 3:  Find HCF of  10,20 and 30 .

Solution: Factors of 10 : 1,2,5,10

Factors of 20 : 1,2,4,5,10,20

Factors of 30 : 1,2,3,5,6,10,15,30

So, the common factors of 10,20 and 30 are:1,2,5,10

HCF = 10

Sample Questions
(More Questions for each concept available in Login)
Question : 1

M and N are co-prime numbers, M is lowest even prime number and N is lowest odd prime number. Which one of the following is their product ?

Right Option : A
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Explanation
Question : 2

H.C.F of 36 and 144 is ____________

Right Option : A
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Explanation
Question : 3

HCF of 24, 36 and 56 is ________________

Right Option : D
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Explanation
 
 


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