Math Arguments

Dividing a Number by UmberN

Can you find a number such that,

if you move the leading digit to the units place of a number, i.e. 72 becomes 27 or 381 becomes 813, the original number is a factor or multiple of the new number? Oh, and not all digits are identical.

1. Can you find a two digit number that will work in this way?

2. If you can't, was it because it can't happen?

3. In his tweet, James Tanton claims that there are no three or four digit digit numbers that will work. He doesn't make a statement like that unless he has found some way to show it NEVER works. Can you find that rule?