H.C.F. (Highest Common Factor)

What is HCF?

The full form of HCF is Highest Common Factor. The HCF of 2 or more numbers is the highest number which is a common factor of all the numbers.

For example: Let’s say we have 2 numbers: 48 and 66. What will be the HCF for these 2 numbers? The answer to this question is 6.

Now let’s see how we can find out the HCF of 2 numbers. 2 methods for finding out HCF of 2 numbers are:

1. the prime factorization methods
2. the division method

The prime factorization method

This involves

1. the factorization of the 2 numbers and writing them down as the product of their prime factors.
2. identifying the common factors in both the numbers
3. calculating the product of the the common factors

Let’s take 48 and 66 again. Breaking down the 2 numbers into their smallest factors we get

From the set of factors of 48 and 66 it is evident that only 2 (1 instance) and 3 (1 instance) are the common factors. So the H.C.F of 48 and 66 is 2 x 3 = 6

The division method

The involves finding out the HCF by the method of division

1. Divide the numbers by the lowest possible prime number, which is a common factor to both. (here it is 2)
2. Write down the quotients in the next line (here it is 24, 33)
3. Continue dividing by prime numbers which are common factors until the quotients are mutually prime (common factor is 1).
4. Multiply the common prime numbers (left of the ‘)’ ) used for factoring to get the HCF.