CMYK Grey
It’s important understand the difference between CMYK and RGB. Resume, CMYK is ink and RGB is light.
If you need CMYK pure grey colours the values will be:
C: 50% M:40% Y:40% K: this value depends of the intensity of your final grey (darkness K: 100% lighter K:0%)
Easy, really? My tool is illustrator > colour > CMYK panel
Other option is this other panel, select you grey
Now, check one more time the values in CMYK and Voila! the CMY are 0% and K (black) change with a new percent.
In my point of view, this is the better option, more efficient, ecological, cheap and faster. Next time when you create a grey document in CMYK check this values. Little details will be a big work and create more conscience about the impact of your work in the world.