SOLUTION: when 200 is divided by a positive integer N, the remainder is 5. the number of all possible values of N is: A) 2 B)6 C)8 D)13 E)16 Thank you very much for looking at thi

Algebra ->  Sequences-and-series -> SOLUTION: when 200 is divided by a positive integer N, the remainder is 5. the number of all possible values of N is: A) 2 B)6 C)8 D)13 E)16 Thank you very much for looking at thi      Log On


   

Question 752588: when 200 is divided by a positive integer N, the remainder is 5. the number of all possible values of N is:
A) 2
B)6
C)8
D)13
E)16
Thank you very much for looking at this question. I have worked out that N - 40, but I'm not sure how to continue on from there.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose we divided N into 200 and got quotient Q and remainder 5,
like this:

    Q 
N)200
  N·Q
    5

Then to check that division by multiplying, we'd have
200 = N·Q + 5

or

195 = N·Q

So we just write down all the possibilities for N and Q,
which amounts to writing down all the ways to write 195
as a product of two positive integers:

195 =   N·Q
-------------
195 =   1·195
195 =   3·65
195 =   5·39
195 =  13·15
195 =  15·13
195 =  39·5
195 =  65·3
195 = 195·1

And of course. each of those 8 cases of N gives remainder 5 
when we divide 200 by N:

   195      65      39      15 
 1)200   3)200   5)200  13)200
   195     195     195     195
     5       5       5       5

    13       5       3       1 
15)200  39)200  65)200 195)200
   195     195     195     195
     5       5       5       5

Answer:  8

Edwin