Sorry Tenacious,
I have only just seen your question.
If your question gets overlooked then I suggest you follow these instructions to highlight this fact.
http://web2.0calc.com/questions/instructions-on-reposting_1
I suggest you forget about the fractions.
It is not something of mathematical importance.
Wolfram|Alpha interprets the answer to be 1/4
http://www.wolframalpha.com/input/?i=What+is+the+highest+common+factor+of+1%2F2+and+1%2F4
Honestly I do not think you should be getting hung up over this. ![]()
I shall ask other mathematicians to comment.
Here you go.
https://www.youtube.com/watch?v=Mfk_L4Nx2ZI
Thanks for asking this question. I really enjoyed the video clip.
It starts at the very beginning - explaining what factorial means.
Then if progresses to gamma functions.
so there is something for almost every one.
ALSO
The is a clip from the Numberphile website I'll bet their other clips are just as interesting. ![]()