GATTAI 5 KILLER SUDOKU #1 - INTERMEDIATE LEVEL

Kakuro is a pencil puzzle that looks kind of like a crossword grid but it is filled with number sums instead of words.  The clue to each line is a number so that the numbers in the answer are added to create it.  (example: clue line = 3 with two spaces for the answer, therefore the answer are the digits 2 & 1 in some order.  1+2=3)

I told you about Gattai 5 Sudoku puzzles in a previous post.  Well this puzzle is a Gattai 5 Killer Sudoku, meaning that it not only contains 5 interlinked sudoku grids but it also has elements of Kakuro in it.  The best way to solve these puzzles are to work on the large sums and multipliers first.  Break the multiples down into their prime number multiples to help you find the answers.
           
Rules: Fill in the grids with the digits 1-9 sudoku style.  The digits in each color filled area should be added, subtracted, multiplied, or divided to equal the number in the clue.  Each clue has an operation in it.  For division and subtraction start with the highest number first (example: a region that has the clue 2- could be solved with 6 - 3 - 1).  Digits cannot be repeated within the colored areas.

GATTAI 5 KILLER SUDOKU #1 - INTERMEDIATE LEVEL

HINT: The best place to start this particular puzzle is in the bottom right square.  Only using the digits 1-9 as in any other Sudoku puzzle, you know that 35 = 5 x 7.  To find the 3 digits that multiply to get 144 break down the 144 into it's prime factors. 
144 = 2 x 2 x 2 x 2 x 3 x 3
Possibility 1:  144 = (2 x 2) x (2 x 2) x (3 x 3) = 4 x 4 x 9
Possibility 2:  144 = (2 x 2 x 2) x (2 x 3) x 3 = 8 x 6 x 3
Possibility 3:  144 = 2 x (2 x 2 x 2) x (3 x 3) = 2 x 8 x 9

You know that the answer cannot be the Possibility 1 because there cannot be two 4's in a sudoku square and there cannot be repeated numbers in a colored region.

32 = 2 x 2 x 2 x 2 x 2 broken down into two digits that multiply together only has one possibility
32 = (2 x 2 x 2) x (2 x 2) = 8 x 4

Therefore after all of this you know that Possibility 2 and Possibility 3 both contain an 8 and because there cannot be two 8's in a sudoku 3x3 square the 8 in the 32x region must be out of this 3x3 sudoku square.  So then the 8 is above the 4 in the 32x region so that it can be out of this 3x3 sudoku square.

SOLUTION