Henry Ernest Dudeney/Modern Puzzles/63 - Find the Factors/Solution

by : $63$

 * Find the Factors

Solution

 * $36070 \times 34227$

Proof
We have:
 * $1234567890 = 2 \times 3^2 \times 5 \times 3607 \times 3803$

It is safe to say that one of the factors will contain $3607$ and the other $3803$.

It remains a matter of putting these together with the smaller ones to get the smallest difference.

The remaining factors can be collected as $3^2 = 9$ and $2 \times 5 = 10$

and so to the result.