23822

The shortest route from the yellow square to the end goes round the ring with corners 28, 51, 96, 81, 54, 72, 49, end. We did this in 9 moves. For the first leg there are 9 squares but 9 isn't a factor of 60 so we split it to move 2 first and then 7 (a factor of 14). The next leg was 7 squares, which is a factor of 28, so we did it in one move. Then 3 is a factor of 51 so we went to the next corner. 4 is a factor of 96, which went to the next corner. 3 is a factor of 81, taking us to the next corner. From 54 we had to take 2 moves for the 5 squares. We moved 2 first and then 3, a factor of 87. From 72 it was 4 squares to the next corner, a factor of 72, and then 7 squares to the end and 7 is a factor of 49.