An amazing multiplication puzzle

If you multiply two 5-digit numbers you can get the answer 123456789. Can you guess the two five digit numbers?

This is a very beautiful puzzle and you might think that a big mathematical theory should be hidden behind it. But in fact its beauty is only incidental.

Hints:      'Decompose the number (123456789) into its prime factors'.

            123456789 = 3 x 3 x 3607 x 3803

Solution: 

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123456789 = (3 x 3607) x (3 x 3803) = 10821 x 11409