Division Sudoku

Davis has a new challenge for you.

Division Sudoku:

Everyone loves sudoku (well, maybe not everyone, but most people that read The Davhee Repore), the number placing logic game. Typically the 9x9 sudoku grid has a few numbers filled in and through careful examination of potential solutions you slowly fill in the grid. The puzzles range from mild to diabolical.

This sudoku, however, is different, and some say, tricky. Where other sudokus have a few starter numbers embedded in the puzzle to help you begin your logic, in this sudoku you don't get any numbers. Instead of numbers the puzzle provides the necessary information for a solution through showing the mathematical relationship between two squares. Complete rules are listed below.

None of the concepts needed to solve this puzzle go beyond knowing how to divide and to determine less than and greater than. The puzzle, however, will push the solver to think about the problem in a new way.

Instructions:

1. Fill in the grid so that the numbers 1 through 9 each appear exactly once in each row column, and block.
   
2. In addition, each time a cell's value divides one of its neighbors within a block, the line between the two cells is marked with a red arc shaped like a "C". That indicates that the number in cell A evenly divides into the number in cell B. You can think of this as "A goes into B with no remainder." For example, if you figured out that cell A was 3 then cell B would be 9. (Two hints: 1. The number "1" divides into any of the other numbers. 2.You might want to look for chains. . .that is, groups of cells connected by the red arc.)
   
3. The grid also contains a few greater than (>) symbols to guide your logic.

Good luck!