
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 12th, 2010, 04:29 AM  #1 
Newbie Joined: Sep 2010 Posts: 6 Thanks: 0  Largest integer _1
Hi all, I want to find the largest integer that divides 364, 414, and 541 with remainders R1 , R2, and R3, respectively, such that R2 = R1 + 1, and R3 = R2 + I. Can anybody help me to solve the problem?... 
September 12th, 2010, 04:40 AM  #2  
Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0  Re: Largest integer _1 Quote:
 
September 12th, 2010, 01:19 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1385 
The answer is the greatest common divisor of 414  364  1 = 49 and 541  414  1 = 126. It's easy to see that gcd(49, 126) = 7. The remainders mentioned are 0, 1, and 2. Had the gcd been less than three, there would have been no solution. 

Tags 
integer, largest 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
largest possible value  JC  Calculus  4  September 5th, 2015 06:09 AM 
largest integer  sonu_pal  Algebra  6  September 12th, 2010 12:47 PM 
the largest integer number  rose3  Number Theory  3  March 1st, 2010 06:24 PM 
Why 30 is the largest integer such that none of its....?  Hussam  Number Theory  1  December 30th, 2008 06:45 AM 
Largest y Value  symmetry  Algebra  7  February 18th, 2007 05:18 PM 