Euclid's Division Algorithm:Algebra form

Euclid's Division Algorithm

is also have it's utility in algebra in same formation.

whenever, one intended to perform long Division of algebraic terms then that procedure also follow Euclid Division Algorithm, or I can give you an idea to clear the concept so have a look at this,

when we divide 23 by 5
then this divided as
23/5 = 4 ³/5

here quotient is 4 and remainder is 3.
But to justify this division we tend to multiply quotient to Divisor and result is added to remainder hence
5×4+ 3 =23

this is what can be expressed in generalisation as

B×q+ r = A

What Euclid has given.

On the other aspect of algebra this can be applied similarly likewise.

But the representation is quiet different as each term is considered as polynomial in algebra and represented by P(x) that's why
p(x) is considered as Dividend
q(x) as quotient
r(x) as remainder
and
g(x) as Divisor

so the algorithm will be

p(x) = q(x) × g(x) + r(x)

this is for justification of long Division of algebraic terms.
Alternatively this formula is useful to evaluate any of the polynomial be it quotient​, be it remainder or Divisor​ if all the other three polynomials are given.
Suppose, we've to evaluate q(x), then

q(x) =  [ p(x) - r(x) ]/ g(x).
Now, over to you let me know by comment if I'm missing something.

Euclid's​ Division Algorithm

Hello Knowledge seekers,

Here I'm with Division algorithm given by EUCLID
.

Euclid's Division Algorithm/lemma  

• This is one of the best tool to find HCF.
• Division Algorithm stands for finding or justification of Division and long divisions,

• this algorithm works over concept of 

A = B×q + r

where,

A = Dividend

B = Divisor

q = quotient

r  = remainder

an example of application of rule :-

Q. Using Euclid’s algorithm to find HCF of the 65 and 117.

Solution : 


Step:1 Since 117 > 65 we apply the division lemma to 117 and 65 to get ,
117 = 65 x 1 + 52


Step:2 Since 52 ≠ 0 , we apply the division lemma to 65 and 52 to get
65 = 52 x 1 + 13


Step:3 Since 13 ≠ 0 , we apply the division lemma to 52 and 13 to get
52 = 13 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this Step is 13, the HCF of 117 and 52 is 13. 

so here is how we can find out HCF of any of two Numbers with the help of Euclid's division algorithm.
Still if you are finding any difficulties then comment that, I would like to hear from you.