Question 536705
If all three digits of a three-digit integer are the same, then if 
that integer is divided by the sum of its digits, the quotient
always equals 37.  Why?
<pre>

If that digit is N, then 

(1) the sum of its digits is N+N+N or 3N 

and 

(2) the integer itself is 100N + 10N + N = 111N = (3×37)N = (3N)×37 

Edwin</pre>