How to simplify fractions like 122/163 systematically

[TSN79]

I'm wondering about fractions, and how I can simplify them. If they're small like 6/10, I see it straight away, but if they're big like 122/163, I don't really know where to start without resorting to random trial and error...
Isn't there a more structural procedure to simplify fractions as much as possible?

 

[dmoravec]

the only way I can think of off the top of my head is comparing factors...which is a litle better than trial and error.
ie: factors of 122 include (I'll probably miss some) 1,2,61,122
but the 163 is prime and only has factors of 1,163.
Since no factors (besides 1) overlap the fraction cannot be reduced. But if you had a common factor X then both the top and bottom could be divided by X to get an equivalent but reducded form of the fraction.

 

[chroot]

dmoravec's got it.

Try dividing both top and bottom by small primes -- 2, 3, 5, 7, etc. -- until either the top or bottom is prime, or they share no common factors.

- Warren

 

[StatusX]

You might try looking at the http://en.wikipedia.org/wiki/Euclidean_algorithm" for finding the greatest common divisor of two numbers.

 

[TSN79]

Hey thanks all. That Euclidean algorithm worked like a charm. Fancy.