The digits of a two-digit number “AB” are reversed to form a second two-digit number “BA” and the lesser of the two numbers is subtracted from the greater.  What prime number must be a factor of the difference if ?

 

 

If we look at some examples,

 

 

In general, we can write

 

 

Subtracting

 

 

So the number we are looking for is 3.