Well, you haven't provided any numbers, so I'll invent one and show its rate now.
Let's take 48. Start the rainbow with 1 on the left, a big gap then 48 on the right.
Close to 1 write 2 to the right of 1 and 24 to the left of 48. You can draw rainbow arcs joining 1 and 48, 2 and 24, if you wish.
To the right of 2 write 3 and to the left of 24 write 16. Join 3 and 16.
Carry on in the same way with 4 and 12, and 6 and 8.
You will end up with a 5-arc rainbow: 1-48, 2-24, 3-16, 4-12, 6-8. These are distinct factors.