Star Product Sudoku (Daily Sudoku League #89)

I have created 3 Sudoku variations for preparation for the upcoming 2nd Round of Sudoku Grand Prix Championship 2015 These Sudoku types are Start Product Sudoku, Before 9 Sudoku, and Even Passage Sudoku. Today I wanted to post Even Passage Sudoku as this is the one that has come up with very nice logic, but I saw that Before 9 Sudoku and Even Passage Sudoku is already posted on The League of Extraordinary Ladies and Gentlemen for this week. So I am posting Start Product Sudoku today. Soon I will try to post Even Passage Sudoku. Hope these puzzles will be good practice for the 2nd Round of Sudoku Grand Prix Championship 2015.

This Star Product Sudoku is my is my 89nd contribution for The League of Extraordinary Ladies and Gentlemen. Can you solve this Sudoku Puzzle?

Rules of Star Product Sudoku

Standard Classic Sudoku Rules apply. Additionally, the clues outside the grid indicate the product of the digits placed in the cells containing stars in the corresponding row or column.