SOLUTION: 1)what is the smallest positive integer that is 13 times the sum of it is digits

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Question 934279: 1)what is the smallest positive integer that is 13 times the sum of it is digits

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
It can't be a 4 digit number or larger because 1000/13 = 76.9 
and the largest possible sum of 4 digits is of 9999 which is only 36.

It can't be a 2-digit number because 10x13=130 a 3 digit number.

So it must be 3-digit number:

100h%2B10t%2Bu=13%28h%2Bt%2Bu%29
100h%2B10t%2Bu=13h%2B13t%2B13u
87h=3t%2B12u
29h=t%2B4u
t=29h-4u

0%3Ct=29h-4u%3C=9

h must be 1 because if it were 2 or greater, 
u would have to be greater than 9.

29-4u%3C10%0D%0A%7B%7B%7B4u%3E19
u%3E4.75 

So u  is 5,6, or 7.  It can't be 8 for that would make t negative

t=29-4u
If u=5, t=9, and the number ia 195

If u=6, t=5, and the number is 156  

If u=7, t=1, and the number is 117
 
Answer: The smallest is 117.

Edwin