$\gcd(0.5,2.5)=1$ or $0.5$? So I got this question in my exams. 
Find the HCF of $0.5$ and $2.5$. 
My friends are saying that answer would be $0.5$. 
I wrote $1$ because I couldn't see any factor bigger than it common to both.
Moreover, I have one more point that domain of $\gcd$ is positive integers.  
So there can be two things, whether, the question is wrong, and even if we extend $\gcd(a,b)$ to rational numbers, answer would be $1$, because $1$ is bigger than $0.5$. 
So please clear my doubts. 
 A: This question
has the assumption
that a factor of
a non-integer rational number
can be specified.
In particular,
it assumes that
factors of 0.5 and 2.5
can be specified.
I believe that this shows
a fundamental misunderstanding
on the part of the creator of the question.
The algorithm stated is this:
$HCF(a/b, c/d)
=\frac{\gcd(a, c)}{\operatorname{lcm}(a, c)}
=\frac{\gcd(a, c)}{ac/\gcd(a, c)}
=\frac{\gcd^2(a, c)}{ac}
$.
This does not even use the denominators!
To use Pauli's famous phrase,
this is not only not right,
it is not even wrong.
A: First and foremost, I would ask you to edit your question in order to only present itself as a question. Other details are not only irrelevant but also distracting.
Now, two ways of defining $d=\text{mdc}(a,b)$ are:


*

*$d$ satisfies:


*

*$d | a$, $d| b$

*$ e|a, e|b \implies e | d $



or 


*$d$ is a generator of the ideal generated by $a,b$.


My algebra may be a bit rusty... so these definitions may not be equivalent when dealing with some spaces (for instance, non-PID's), but they are for our discussion here.
There is a problem when we try to apply these definitions for $\mathbb{Q}$. If you check, given any two (non-trivial) numbers, any number will be a $\text{gcd}$ of both. The discussion is quite trivial in $\mathbb{Q}$.
Whereas, in $\mathbb{Z}$, generators of ideals are defined up to a sign (since units are only $1$ and $-1$), hence there is no problem in defining $\text{gcd}$ well enough.
A: I got my answer on my own! After a lot of thinking (elementary terms only), I deduced that the answer is indeed $0.5$. Because,  
first and the foremost, we look at Euclid's Division Lemma, which states that any positive integer $a$ can be expressed as $bq+r$ where $b,q$ and $r$ are integers!  
Now even if we extend this to rational numbers, $q$ will indeed remain integer. (think it over, you will get why, because if it would not have been the case then gcd would have been non-sensical).  
Coming back to my question, $\gcd(\frac12,\frac32)$, if we take $1$ to be the common factor, $1$ is not a common factor because on dividing $\frac12$ by $1$, we get a fraction, not an integer. Same with $\frac32$. And the largest number satisfying this rule (quotient is an integer) is indeed $0.5$. 
Thus, $$\gcd(\frac12,\frac32)=\frac12$$
P.S.: Sorry, if any one already got there.
