The rythym is Black, Black, Red, Red, Blue, Blue at 208Y120.
This is repeated seven times in the typical three phase panel of 42 circuits.
So...
1,2 Black
3,4 Red
5,6 Blue
The colors shift if we're talking 480Y277
But the rythym stays the same.
IMHO this is the easiest way for you to do it. You are on the right path with the divide by six and then use the above chart with the remainder. I only added one change to it though.
1,2 Black **** Brown
3,4 Red **** Orange
5,0 Blue **** Yellow
You divide the circuit number in question and then use the remainder to find the circuit color.
ex.
Circuit 64
64/6 = 10 full times with a remainder of 4. Check the chart and 4 is red or orange.
Circuit 30
30/6 = 5 full times with no remainder so the 0 is used.
So it is a Blue or Yellow circuit.
Circuit 87
87/6 = 14 full times with a remainder of 3. 3 is also a red or orange circuit.
I hope I explained as close to the way I learned it. Seems easy for me, may not for others. Great part of this trade is we take from others things we can use, and sometimes it works and sometimes it doesn't.
LMK if I can explain it any better.
Philip