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How to solve Euclidian program in python?


**THE PROBLEM**

The euclidian algorithm calculates the greatest common divisor (gcd) of two
integers a and b. pgcd (a, b) is the largest integer p that divides a and b, knowing that:
- If a is divisible by b, pgcd (a, b) = b.
- Otherwise, by setting r the remainder of the integer division of a by b, pgcd (a, b) = pgcd (b, r)
By setting q the quotient of the integer division of a by b, let us calculate for example the gcd of 90 and of
35 (gcd (90,35), so a = 90 and b = 35):
a = b × q + r
As for 90/35 we have q = 2 and r = 20, then 90 = 35 × 2 + 20
**According to Euclid, pgcd (90.35) = pgcd (35.20). So we start over with the new values:
35 = 20 × 1 + 15
According to Euclid, pgcd (35.20) = pgcd (20.15). So we start over with the new values:
20 = 15 × 1 + 5
According to Euclid, pgcd (20.15) = pgcd (15.5). So we start over with the new values:
15 = 5 × 3 + 0
15 is divisible by 5 so we stop and pgcd (15.5) = pgcd (20.15) = pgcd (35.20) = pgcd (90.35) =
5.**
Write the code of the euclid function (a: int, b: int, verbose: bool = False) -> int
which calculates the gcd of a and b and, if the verbose parameter is True, displays the different steps of
the algorithm of the calculation (the values ​​of a, b, q and r).

What I’ve done (it’s false i know, idk how to do this…)

 def euclide(a,b,verbose = False):
    
    r=a%b
    q=a//b
    
        
    
    if a%b == 0:
        verbose = True
        print(a)
        print(q)
        print(r)
        return b
        
    else:
        
        while r != 0:
            a = b 
            b = r
            a = b * q + r
print(euclide(90,35))
       

Idk how to get the bold part above in the program

I couldn’t tell but I have no idea how to do this, even the related posts are not that related to this and don’t answer the question…

Thanks



Source: https://stackoverflow.com/questions/70559714/how-to-solve-euclidian-program-in-python

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