Question 888656
<pre>
The answer is 0 and the shared number is 0.

That's because if the all pick a 0 the product will be 0.

For instance: 

the 1st person could pick the numbers 0,1,2,3, and 0×1×2×3 = 0
the 2nd person could pick the numbers 0,4,5,6, and 0×4×5×6 = 0
the 3rd person could pick the numbers 0,7,8,9, and 0×7×8×9 = 0

They all share only one number, 0, and their products are all 0.

Edwin</pre>