Is there any flexibility in the size of the center rectangle?
If so, perhaps you could start from the outside edges and work in to the center?
If you start with a 'finished' size where length and width are easily divided by the same number, that would make the process easier.
Examples:
50 x 60 - both numbers evenly divisible by 2, 5, and 10
48 x 60 - both numbers evenly divisible by 2, 3, 4, 6, and 12
52 x 60 - both numbers evenly divisible by 2, and 4
51 x 60 - both numbers evenly divisible by 3
Could you put small borders around your center section to get it to a more accommodating size?