SOLUTION: A number N divides each of 17 & 30 with the same remainder in each case. What is the largest value N can have?

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?
---------
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.
RELATED QUESTIONS
When a whole number N is divided by 2, the remainder is 0. When N is divided by 3, the... (answered by jim_thompson5910,Edwin McCravy)

When 655, 528 and 698 are in turn divided by a certain number, the remainder is 5 in each (answered by Alan3354)

What is the greatest number of 5 digits which when divided by 16, 24, 30 and 36, 10 will... (answered by ikleyn)

1.The product of two numbers is 8000. If LCM of two numbers is 800, find HCF? 2. Find... (answered by ortarico)

The number n is a two digit number. When n is divided by 10 the remainder is 9, when n is (answered by ankor@dixie-net.com)

Use mathematical induction to prove each of the following: Fore each natural number n, (answered by richard1234)

This is a Number Theory proof: If N = abc + 1, prove that (N, a) = (N, b) = (N, c) =... (answered by KMST)

if N is divided by 7 the remainder is 4 and if same number N is divided by 8 the... (answered by ramkikk66,KMST)

Could someone help me with Exponents? I have two scenarios. Thanks. Do exponential... (answered by stanbon)