SOLUTION: the numbers 203 and 298 divided with the positive integer x leave remainder 13. what is the sum of the possible values of x?

Algebra ->  Decimal-numbers -> SOLUTION: the numbers 203 and 298 divided with the positive integer x leave remainder 13. what is the sum of the possible values of x?      Log On


   

Question 280685: the numbers 203 and 298 divided with the positive integer x leave remainder 13. what is the sum of the possible values of x?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
To state you have a remainder of 13 implies that you divided by a number greater than 13.
.
Since we need to a remainder of 13, we need to find the numbers that are an equal multiple of 'x'.
.
203 - 13 = 190
298 - 13 = 285
.
What is the greatest common factor of 190 and 285?
.
190 = 2*95
285 = 3*95
.
So the denominator 'x' is 95:
203/95 = 2 R 13
298/95 = 3 R 13
.
Answer:
The positive integer 'x' equals 95.
.
Done.