### Number guessing puzzles

The first beautiful puzzle was by Yukio Yamamoto in Japan:

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

And the second, very similar puzzle:

### HINT

Decompose the numbers into their prime factors to help you solve the puzzles.

123456789 = 3 x 3 x 3607 x 3803

and

123456784 = 2^{4} x 11^{2} x 43 x 1483