Finding a Number

Date: 4/13/96 at 16:47:51
From: Anonymous
Subject: Number Riddles

My ones digit is twice my tens digit.  One of my factors is 3.  
What am I?

Date: 4/17/96 at 13:0:32
From: Doctor Joshua
Subject: Re: Number Riddles

Hi!

I was just staring at this problem when I realized 12 works.  And 
then it occurred to me that 24 works, and 36, and even 48.  But 
that's all the tens that work (and it has to be because if one 
existed that was in the sixties, its unit digit would have to be 
12!).  Then there are hundreds, and by process of elimination, 312 
works, then so do 324, 336, etc. By analogy 612 etc. works, and so 
does 912 etc., and on, and on.  I hope this is what you were 
asking.

-Doctor Joshua,  The Math Forum