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A question to ponder on factors

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A question for discussion on factors

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When does a factor have to be positive or even a whole number.  And when does 1 count?

The factors of 18 are 1,2,3,6,9 and 18.   What about the negatives of these?

If I am asked to factorise      $${\frac{{\mathtt{x}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{y}}}{{\mathtt{3}}}}$$    then the answer would be   $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)$$   so the fraction is classed as a factor.

By this logic    $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$    is also a factor of  2 because   $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{2}}$$

That is, 1/3 goes into 2 an integer 'whole' number of times.

Dec 18, 2014

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Thanks for this Melody!

Dec 18, 2014
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I posted this some time back.  Only happy7 commented.

Did no-one else find it worthy of comment?

Anyway, I stumbled across it and I thought I would bump it and see if I get any response before I let it retire into oblivion.

Jan 5, 2015