I'm taking 'Introduction to Mathematical Thinking' on Coursera platform and following proof steps are given : 

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> Proof of $\sqrt{2}$ is irrational.
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> Assume $\sqrt{2}$ is rational. $\sqrt{2}=p/q$
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> p and q have no common factors.
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Why do p and q have no common factors? Is this a consequence of a property of the rational numbers? As p and q can be rational numbers we can set p = 6, q = 9 so p, q have common factors?