
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 11th, 2010, 10:12 PM  #1 
Newbie Joined: Sep 2010 Posts: 6 Thanks: 0  largest integer
hi all, i want to Find the largest integer that divides 364, 414, and 539 with the same remainder in each case... can u just help me solving this problem...please provide complete explanation... 
September 11th, 2010, 10:45 PM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
We have 364 = BQ_1 + R, 414 = BQ_2 + R and 539 = BQ_3 + R, where B is the largest integer we wish to determine and R is the same remainder in each case.

September 11th, 2010, 11:01 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: largest integer
I wrote a short program on my TI89, and found that 25 is the largest integer that divides the three numbers with a remainder of 14 in each case. 
September 11th, 2010, 11:26 PM  #4 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Okay. Can you prove that B = 25 using paper and pencil?

September 11th, 2010, 11:33 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 466 Math Focus: Calculus/ODEs  Re: largest integer
No, and my approach was very similar to yours, but I found too many variables and not enough equations. That's why I resorted to brute force rather than finesse. I would be interested to learn how it is done with pen and paper. 
September 12th, 2010, 12:02 AM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,805 Thanks: 1045 Math Focus: Elementary mathematics and beyond  Re: largest integer
539  14 = 525, 414  14 = 400, 364  14 = 350, so 25 divides 539, 414 and 364 with a remainder of 14. Now you can check if 539  1, 414  1, 364  1; 539  2, 414  2, 364  2 and so on up to 539  13, 414  13, 364  13 have a common divisor that is greater than 25. (I used a calculator to check them). 
September 12th, 2010, 12:47 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,951 Thanks: 1599 
The required integer is the greatest common divisor of 414  364 = 50 and 539  414 = 125. It's easy to see why, and to find that gcd(50, 125) = 25. 

Tags 
integer, largest 
Search tags for this page 
find the greatest number that divides 364 414 and 539,greatest num that divides 364,414,जिसका भाग 364, 414, 539, में देने पर प्राप्तांक,find the greatest number that divides 364 414 and 539 with the same remainder in each,greatest counting number divides 364, 414, 539 with same remainder
Click on a term to search for related topics.

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 _1  sonu_pal  Algebra  2  September 12th, 2010 01:19 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 