In this post we will understand the continuous division method to find the hcf of two numbers say we want to find the hcf of 24 and 36 this method is generally used for large numbers
But first, let's try it out with smaller ones
As the name says we have to use division
In the first step we divide the greater number by the smaller number
Here 36 is the greater number so we divide 36 by 24 we are generally used to writing the quotient on top
But in this method we will write like in the image
24 x 1 is 24 and 36 minus 24 is 12
But wait, we're not done yet the name says continuous division
This was just the first part we got the quotient as 1 and the first remainder as 12
We call this the first remainder as we get many remainders in this method
In the second step we divide the smaller number by the first remainder
The smaller number is 24
So we write 24 there
We are dividing the smaller number by the first remainder 12 times 2 is 24
And 24 minus 24 is 0 we continue this till we get the remainder as zero and guess what we already have the hcf
The final divisor becomes the hcf so here the hcf will be 12
the hcf of 24 and 36 is 12
We divide continuously till we get the remainder is 0 this part was a first division
And this was a first remainder
Since it was zero, we perform the second division
In which the smaller number became the dividend
And we continue this Till we got 0
But wait, what if they wouldn't have got a zero here what would be the next dividend let's look at another example to understand that
We try to find the hcf of 1044 and 1512 in the first step we divide the larger number by the smaller number
That is, we divide 1512 by 1044
1044 times 1. is 1044 one is the largest Quotient possible here since 1044 times 2 is 2088 which is greater than 1512
And 1512 minus 1044 is 468 this becomes a first remainder
Since it's not zero, we continue with that division the smaller number becomes the next Dividend
And the first remainder becomes the Divisor
So we write 1044 and then we write 468 times 2 equals 936
And 1044 minus 936 is 108
Now we completed the second stage and the remainder is not 0 so how do we continue further well, it's easy the first remainder becomes the divided
And the second remainder becomes the divisor
we can write the next step as r1 divided by r2
The first remainder is 468 so we write it this is r1 divided by r2 this is the 3rd division we are performing for this example
468 times 4 equals 432 and 468 minus 432 is equals to 36 the remainder is still not 0
The next step is simple it will be our R2 divided by R3 108 is the second remained and 36 is the third remainder
Hence we write the second remainder, which is 108 here
We are dividing R2 by R3
36 times 3 is108 and finally we get the remainder at zero
That's where we stopped and the final divisor becomes the hcf hence the hcf of 1044 and 1512 is 36
There is another way in which you can look at it, look at the first example
If the remainder is not 0 the divisor becomes the next dividend, it's the same thing in the second example where we performed for division processes one two three and four
The first remainder was non zero 1044 became the next dividend
Then 468 became the next devident
Since was not zero and then 108 it became the next devident
and we stopped since the remainder became 0 and for every division process the remainder is the divisor and remember once you get the remainder at zero the final Divisor becomes the hcf
