Question 1200301: A three-digit number is divided by the sum of its digits. What is the smallest
possible quotient?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
To get the smallest possible quotient, we want the 3-digit number to be relatively small, and we want the sum of the digits to be large.
Logical analysis suggests that the number we are looking for is 199.
The first digit is the smallest possible; and given that first digit 1, the largest possible sum of the digits is if the last two digits are both 9.
I made an excel spreadsheet to look at the quotients for all 3-digit numbers; it verified that in fact the smallest possible quotient is if the 3-digit number is 199.
ANSWER: 199/19
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