I started by working out where to place the Red 5 and 4 cards because they were not factors of any numbers on the blue cards. The only way to include a red 5 card as a factor was to place it at the beginning or end of the sequence next to the blue 5 card. I decided to place the two 5 cards at the start.
Next I worked out that the same logic that I used with the 5 cards would also apply to the Number 4 cards. I decided to place the no.4 cards at the end of the sequence.
By now my sequence was 5 5 _ _ _ _ _ 4 4 ( starting and ending with Red card)
Next I worked out that the Red 1 card should be put next to the Blue 5 card since 1 is a factor of every number possible. ( 5 5 1 _ _ _ _ 4 4 )
I also worked out that the Blue 6 card must be placed between the Red 2 card and 3 card. ( 2 6 3 or 3 6 2 ). Therefore the Red 3 card must be placed between the Blue 6 card and Blue 3 card, since it is not a factor of any other cards. Also, the Red 2 card must be placed between the Blue 6 card and Blue 4 card, since it is only a factor of those two cards
After working all of that out I worked backwards from the Blue card and placed everything in order.
The final result was 5 5 1 3 3 6 2 4 4. ( Starting and ending with Red card )