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?

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) (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.
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Since we need to a remainder of 13, we need to find the numbers that are an equal multiple of 'x'.
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203 - 13 = 190
298 - 13 = 285
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What is the greatest common factor of 190 and 285?
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190 = 2*95
285 = 3*95
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So the denominator 'x' is 95:
203/95 = 2 R 13
298/95 = 3 R 13
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Answer:
The positive integer 'x' equals 95.
.
Done.
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