### 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:

### SOLUTION

The answers are:

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

and

123456784 =(2 x 11^{2} x 43) x (2^{3} x 1483) = 10406 x 11864