Closer

Title: Closer

Rating: 3/5

This blog has been publishing puzzles for one year, which means we're just under the halfway point for how many puzzles I've created.  In this puzzle, the usual product rules apply, with one extra rule to make this even more Sudoku-like.  See the alteration in the first rule below.

The official rules:

• The digits 1 through 9 appear in each row, each column, and each three-by-three grid exactly once.
• Digits in each shaded region must multiply to the indicated product.   
• Squares with multiple colors contain a number that’s used in the product for adjacent regions of each of those colors.  
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.