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.