Rossicoe

I've got yet another method if interested :

I´d go another route in this particular case:
In essence it´s the partial angled circle assign color rotate 45° - doubled - assign color - double - assign color etc.....
 

Rossicoe, just like PixelPest suggested you could use the conical gradient but with the center in the center of the circle.  Use a start and stop point in the gradient for every color and if you zoom in when placing them so that they are really close the transition will be pretty sharp.
Or, you can make wedges used behind a clipping mask of the circle.
There are other ways but the top is probably the easiest.  Personally I like the bottom better but it's a bit more work.  And under the right conditions you could have an antialiasing issues.  Pluses and minuses in all ways.
Hope that helps.
Circles.afdesign
 

Just a small hint. If you want a sudden color change you can try Type: "Conical" instead of "Linear" and place the middle point outside the circle - otherwise there will be a interpolation/transition where the color changes:
 
Cheers
P.