Question

is there anyone can tell me something about Euclidean algorithm ?

Answer 1

if a and b are both non zero then they have a unique greatest common divisor (gcd) where you can form an equation c=ma=nb as an intetger linear combination of a and b

Answer 2

for example gcd(48, 27) let a =48 b=27
you get 48=1(27) = 21
27=1(21) + 6
21=31(6) +3
6 = (2)(3) + 0

gcd(48,27) = 3

Answer 3

Sure, buddy. The Euclidean algorithm is a simple method for discovering the greatest common factor (GCF) of two numbers.
To perform the method, given two numbers, simply take the smaller number and subtract it from the larger number. Repeat this process until the result is two matching numbers, and that result is the GCF of the two.

Example: Find the GCF of 645 and 395
645-395 = 250
395-250 = 145
250-145 = 105
145-105 = 40
105- 40 = 65
65-40 = 25
40-25 = 15
25-15 =10
15-10 = 5
10-5 =5
5, 5
so the GCF of 645 and 395 is 5.