Equal Product Sudoku Variation: Math-Based Logic Puzzle

Equal Product Sudoku appeared recently in the Math Variation Sudoku Mahabharat 2016 round. I created this puzzle while practicing for this championship. Equal Product Sudoku is a very interesting Sudoku variation in which diagonally touching numbers have the same product as other diagonally touching numbers in the same 2x2 square. One has to be very careful while solving this Sudoku type, as multiplying numbers can have many different combinations, and missing even a single combination will lead to getting the wrong solution. Today's Equal Product Sudoku is a very interesting puzzle that requires a lot of calculations to be done before putting in the first few numbers. After putting in some numbers, the puzzle will proceed. However, variation rules are used till the end. This is a tough puzzle and is only for experienced players. Beginners should try to avoid solving this puzzle, as they will find this puzzle very tough. One way to solve this puzzle, I found that first place the prime numbers like 5 or 7, as these numbers cannot be part of the equal product region. Once a few of these prime numbers are marked, then one can proceed to see the possibilities that satisfy the equal product equations.

This Equal Product Sudoku puzzle I am posting in The League of Extraordinary Ladies & Gentlemen as the 156th Sudoku in this series. Can you solve this Sudoku puzzle?

Rules of Equal Product Sudoku

Standard Classic Sudoku Rules apply. Additionally, intersections marked with 'X' indicate that the product of digits in diagonally opposite cells is equal. Not all possible Xs are marked.