We looked for the shortest number of moves taking us round one of the larger routes. The one we found used 15 moves using the following corners: 60, 28, 36, 56, 30, 24, 28, 48, 98, 76, 4, 40, 12, end. We didn't treat 20 as a corner (between 48 and 98) because it was not coloured green.
We moved 4 to get to 25 and then 5 to get to 28. Then we moved 4, a factor of 28, to get to 36 and then 6 to get to 56. All of the next legs could be done in one move because 7 is a factor of 56, 6 is a factor of 30, 6 is a factor of 24, 4 is a factor of 28, 4 is a factor of 48, 2 is a factor of 98, 4 is a factor of 76, 2 is a factor of 4, 4 is a factor of 40, 3 is a factor of 12 and 7 is a factor of 49. That got us to the end!
If we had counted the red 20 as a green corner, we would have had 1 more move - 2 is a factor of 48, taking us to 20, and 2 is also a factor of 20, taking us to 98.