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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: 20,747 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, 02:39 PM   #5
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Quote:
 Originally Posted by John Travolski I think that I forgot to specify that above.
The question appears here (question 14) without such a specification.

 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.

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