Question 57279: A number N divides each of 17 & 30 with the same remainder in each case. What is the largest value N can have?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A number N divides each of 17 & 30 with the same remainder in each case. What is the largest value N can have?
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If N divides 17, 17=aN+x where x is the unknown remainder.
If N divides 30, 30=bN+x where the remainder is the same.
Subtract the 1st from the 2nd to get:
13=(b-a)N
Since 13 is prime N=13 or N=1.
We want N to be the largest divisor.
So N=13.
Check is out:
17 divided by 13 leaves a remainder of 4
30 divided by 13 leaves a remainder of 4
Cheers,
Stan H.
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