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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: 20,472 Thanks: 2039 
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: 7,932 Thanks: 1126 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: 20,472 Thanks: 2039 
I used a Google search.


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