Divisor puzzle

Here’s an interesting puzzle that you can do with a pack of cards. Start with the cards 1, 2, …, N, where N is some whole number. If you’re doing this with cards, then you might count the Jack as 11, the Queen as 12, King as 13. Let’s say, for purposes of this example, that N=5, so you start with the Ace, 2, 3, 4 and 5 of diamonds (Ace being 1). The aim of the puzzle is to play all the cards to the table obeying the following rules:

1. The first card played must be the highest card, the 5 of diamonds in this case.
2. Subsequent cards can only be played if they are a divisor of the cumulative total of the cards currently on the table. A divisor is a smaller number that evenly divides a larger number.

In the present example, a valid sequence of plays would be 5 (5), A (6), 2 (8), 4 (12), 3 (15), where I’ve put the cumulative total in brackets afterwards.

It gets progressively harder as N gets larger. Also, for N>13 you tend to run out of cards, so you have to do it in your head! I got up to N=23. How high can you go? Maybe post your solutions below so that we can compare.