How do you find the greatest common factor of a series of numbers with decimals?

By "numbers with decimals" you mean non-natural numbers? A greatest common factor is usually used for naturals only.

You can, however, find something similar, as long as all of the number are rational. I'm not sure of the terminology, but you can find the "greatest common measure" between any two rationals, meaning the largest number that divides evenly into both.

 

If in fractional form, just get a common denominator, then find the GCF of the numerators. For example, start with 5/12 and 2/5. These become 25/60 and 24/60. 24 and 25 are relatively prime (have no common factors other than 1 and -1), so their GCF is 1, and so the greatest common measure of 5/12 and 2/5 is 1/60.

 

In decimal form it's basically the same thing, only easier, since finding a common denominator is just a matter of adding zeros. Take 1.24 and 8.4. 1.24 goes out to the hundredths' place, so your common denominator is 100, making 124/100 and 840/100 (notice the extra zero: 8.4=8.40=84/10=840/100). Then you just find the GCF for 124 and 840, which happens to be 4. So your greatest common measure is 4/100, or 0.04, or 1/25.