How does one simplify a complicated ratio?

Question

Is there a simple way to simplify a ratio down? For example 1875:5625:625 would become 3:9:1.

I am using Python, but I'd like to know why and not just how.

Answer 1

Edit: Please note that fractions.gcd has been Deprecated since Python 3.5: Use math.gcd() instead.

There's a built-in gcd function in the fractions module so utilizing it I was able to get decent output:

from fractions import gcd

ratio = '1875:5625:625'

def solve(ratio):
    numbers = [int(i) for i in ratio.split(':')]
    denominater = reduce(gcd,numbers)
    solved = [i/denominater for i in numbers]
    return ':'.join(str(i) for i in solved)

ratio_2_solve =  solve(ratio)
print ratio_2_solve
#3:9:1

So given the ratio

1875:5625:625 

It would produce :

3:9:1

But that's not the best part of it, you could even put ratios like:

'1875:5625:625:5000:46875:46250'

And still get the output of:

3:9:1:8:75:74