CLASS-6
FINDING HIGHEST COMMON FACTOR BY DIVISION METHOD

FINDING HCF BY DIVISION METHOD -

The division method, also known as the long division method, is another technique to find the highest common factor (HCF) or greatest common divisor (GCD) of two or more numbers. This method involves repeatedly dividing the larger number by the smaller number and using the remainder to continue the division process. Here's how you can use the division method to find the HCF/GCD:

Example.1) Find the HCF of 48 and 60 using the division method.

1. Step.1) Divide the larger number by the smaller number. 60 ÷ 48 = 1 with a remainder of 12.
2. Step.2) Now, divide the divisor from the previous step (48) by the remainder (12). 48 ÷ 12 = 4 with no remainder
3. Step.3) Continue dividing the previous divisor (12) by the new remainder (0). 12 ÷ 0 (Since the remainder is 0, we stop here.)
4. Step.4) The last non-zero remainder obtained in the division process is the HCF. The last remainder is 0, so the last non-zero remainder before that was 12.

So, the HCF of 48 and 60 is 12.   (Ans.)

The division method can be a straightforward way to find the HCF/GCD of numbers, especially when the numbers are not too large. However, it might be less efficient for larger numbers compared to other methods like prime factorization. Nonetheless, it's a useful method to understand the concept of finding the common divisor by repeatedly dividing the numbers and using the remainders.

Example.2) Find HCF of 36 and 150 

Ans.)

           36 ) 150 ( 4       [Divide large number by small number]  

                 144

             __________

                   6 ) 36 ( 6    [Divide first divisor by reminder]

                       36

                    _______

                        0     [Reminder zero '0', so stop here (last divisor)]

HCF of 36 & 150 is 6  (Ans.)

Example.3) Find HCF of 12, 18, and 46.

Ans.) Fist we will find HCF of 12 & 18, and we find -

      12 ) 18 ( 1           [Divide large number by small number] 

           12

        _______

            6 ) 12 ( 2       [Divide first divisor by reminder]

                12

             _______

                 0           [Reminder zero '0', so stop here (last divisor)]

Now, we will find the HCF of 6 & 46, and we find -

     6 ) 46 ( 7           [Divide large number by small number] 

         42

     _________

          4 ) 6 ( 1        [Divide first divisor by reminder]

              4

           _______

              2 )  4  ( 2   [Divide second divisor by reminder]

                   4

                _______

                   0       [Reminder zero '0', so stop here (last divisor)]

The HCF of 6 & 46 is 2.

So, the HCF of 12, 18, and 46 is 2.  (Ans.)