My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 11th, 2010, 11:12 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...
sonu_pal is offline  
 
September 11th, 2010, 11:45 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.
johnny is offline  
September 12th, 2010, 12:01 AM   #3
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,155
Thanks: 463

Math Focus: Calculus/ODEs
Re: largest integer

I wrote a short program on my TI-89, and found that 25 is the largest integer that divides the three numbers with a remainder of 14 in each case.
MarkFL is offline  
September 12th, 2010, 12:26 AM   #4
Senior Member
 
Joined: Apr 2007

Posts: 2,140
Thanks: 0

Okay. Can you prove that B = 25 using paper and pencil?
johnny is offline  
September 12th, 2010, 12:33 AM   #5
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,155
Thanks: 463

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.
MarkFL is offline  
September 12th, 2010, 01:02 AM   #6
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,641
Thanks: 959

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).
greg1313 is offline  
September 12th, 2010, 01:47 PM   #7
Global Moderator
 
Joined: Dec 2006

Posts: 18,145
Thanks: 1418

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.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
integer, largest



Search tags for this page
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 07:09 AM
Largest integer _1 sonu_pal Algebra 2 September 12th, 2010 02:19 PM
the largest integer number rose3 Number Theory 3 March 1st, 2010 07:24 PM
Why 30 is the largest integer such that none of its....? Hussam Number Theory 1 December 30th, 2008 07:45 AM
Largest y Value symmetry Algebra 7 February 18th, 2007 06:18 PM





Copyright © 2017 My Math Forum. All rights reserved.