What is the Highest Common Factor (H C F) of two or more numbers?

The Highest Common Factor which is shortened as H.C.F of two numbers is the highest number in the set of Common Factors.

Helping students find the H.C.F of numbers, say 24, 36 and 48; three methods could be employed and they are as follows:

i) Using set of factors        ii) Using prime factorization        iii) Using common division.

Method 1: Using set of factors

NB: Having problems on Factors of Numbers, Visit: what is a Factor of a number? on my blog for clarification. Now,

Set of factors of 24 = {1, 2, 3, 4, 6, 8, 12, 24}

Set of factors of 36 = {1, 2, 3, 4, 6, 12, 18, 36}

Set of factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

Go ahead find the Set of Common Factors = {1, 2, 3, 4, 6, 12}

Therefore the highest common factor = 12.    Hence H.C.F of 24, 36, and 48 is 12.

Method 2: Using prime factorization

Hint: Using the knowledge of indices to represent prime factorization.

24        =          2 x 2 x 2 x 3    =          2³ x 3

36        =          2 x 2 x 3 x 3    =          2² x 3²

48        =          2 x 2 x 2 x 2 x 3 =       2⁴ x 3

Now it can be seen that 3 is common to all factorization, 2² is also common to all factorization. Hence the H.C.F = 2² X 3 = 12

Method 3: Using common division

NB: No number can go into 2, 3, and 4 at the same time, hence H.C.F is 12.


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