Because Graph Three Colouring[0][1] is NP-Complete[2][3] we can use it to solve any NP problem.  Integer factoring is an NP problem[4] so we should be able to factor integers by using Graph Three Colouring.<p>This post shows one way of doing that, and explains the techniques used to show directly that Graph Three Colouring is NP-Complete.<p>[0] <a href="http:&#x2F;&#x2F;www.solipsys.co.uk&#x2F;new&#x2F;GraphThreeColouring.html?HN_20151223" rel="nofollow">http:&#x2F;&#x2F;www.solipsys.co.uk&#x2F;new&#x2F;GraphThreeColouring.html?HN_20...</a><p>[1] <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=10758236" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=10758236</a><p>[2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;NP-completeness" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;NP-completeness</a><p>[3] <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?feature=player_embedded&amp;v=YX40hbAHx3s" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?feature=player_embedded&amp;v=YX40...</a><p>[4] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Integer_factorization#Difficulty_and_complexity" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Integer_factorization#Difficul...</a>