Proving the Property: Relatively Prime Factors and Division

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If pq=ab where p, b are relatively prime, p must be a factor of a and b must be a factor of q.
 
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well, since ab = pq, p divides ab. but (p, b) = 1 and so p must divide a [this is obvious, trust me. if you don't see it, break them up into prime factors and deal with them case by case]. the other direction is symmetric.
 

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