GCD: Fastest Method to Simplify Fractions

[Petrus]

Hello,
I wounder if there is more method Then using euclides algoritmen to solve this problem
Simplifie/shorten(I Dont know how to say in english) $$\frac{196707}{250971}$$ and I get GCD=6783 and get the answer $$\frac{29}{37}$$ is there more method? Is there à method that is a lot more faster Then this one and that method you take out all prime number?

 

[Ackbach]

Check out the Trachtenberg Speed System of Basic Mathematics. There's a novel way of dividing numbers by others numbers of arbitrary length quickly.

 

[mathbalarka]

There's a novel way of dividing numbers by others numbers of arbitrary length quickly.

How does division helps to simplify a fraction?

Is there any method that is a lot more faster than this one

I don't see why you think Euclid's method is slow, can elaborate your logic a bit? Well, you might want to look at the Binary GCD algorith then since it shorten the work of finding the GCD quite a bit.

 

[Petrus]

How does division helps to simplify a fraction?
I don't see why you think Euclid's method is slow, can elaborate your logic a bit? Well, you might want to look at the Binary GCD algorith then since it shorten the work of finding the GCD quite a bit.

Naa its not really hard, I was just looking for more method to solve it :)

 

[Ackbach]

How does division helps to simplify a fraction?

Each step of the Euclidean algorithm is a division problem, is it not? If you can speed up each step of Euclid's algorithm, then you speed up Euclid's algorithm.