elementary number theory - Show that for a and b non-zero integers and c different from zero, then gcd(ca,bc) = |c|gcd(a,b)

Sunday, 18 December 2016

elementary number theory - Show that for a and b non-zero integers and c different from zero, then gcd(ca,bc) = |c|gcd(a,b)

I did:

$$ca = cb * k + r \Leftrightarrow \\
ca - cb*k = r \\
c(a-bk)=r \\
a-bk = r/c \\
a = bk +r/c$$

So, $gcd(a,b) = r/c$

What do I do next?

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