Normal sudoku rules apply. Within cages, digits cannot repeat. Each cage has a value equal to the sum of all the digits it contains. Color each cage 1 of 4 colors. Cages of the same color cannot share sides, though they may touch corner-to-corner. All cages with the same color have sums whose prime factorizations contain the same set of prime factors. [E.g. If a red cage is 20 = 2x2x5, then all other red cages must have a prime factorization of 2^X*5^Y. For example, 10, 20, 40, 50, 80, 100, etc could all be valid. 25 would not be valid (no 2's). 30 would not be valid (2x3x5 has a 3). Any other colored cage could not have a 2 nor 5 in its prime factorizations.]