SOLUTION: 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?

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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?
Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
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?

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
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