
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 16th, 2016, 01:43 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Find the Smallest Positive Integer that...
Find the smallest positive integer which has a remainder of 2 when divided by 3, 5, or 7. I know a tactic to find a positive integer that has a remainder of 2 when divided by 3, 5, or 7: 2 + (3×5×7) = 107. However, 107 is not the smallest positive integer that meets this criteria. What's a good tactic that will allow you to find the smallest positive integer? Last edited by skipjack; March 16th, 2016 at 01:48 PM. 
March 16th, 2016, 01:47 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
Obviously, the smallest with the stated property is 2. Why add on 3×5×7 in the first place?

March 16th, 2016, 02:07 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
Sorry, I meant that it was greater than 2. I think that I forgot to specify that above.

March 16th, 2016, 02:15 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,945 Thanks: 1136 Math Focus: Elementary mathematics and beyond 
3, 5 and 7 are coprime, so the smallest number that is divisible by 3, 5 and 7 is 105. Adding 2 to that gives 107, so the smallest possible number meeting the given requirements is 107.

March 16th, 2016, 04:50 PM  #6 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
How did you find that?

March 16th, 2016, 05:23 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
I used a Google search.


Tags 
find, integer, positive, smallest 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Positive definite matrix whose smallest eigenvector is predefined  whitegreen  Linear Algebra  1  September 25th, 2015 05:41 AM 
please find the smallest integer n  Albert.Teng  Algebra  3  December 16th, 2012 06:20 PM 
Smallest positive integer...  Alann  Number Theory  7  November 7th, 2012 08:39 AM 
Find all positive integer solutions of equation systems:  ducnhuandoan  Number Theory  4  May 1st, 2012 04:46 AM 
Find Smallest Integer  pksinghal  Algebra  5  September 19th, 2010 06:16 PM 