Thread: Highest common factor proof

Ive got the question: "For non-zero intergers a, m and n, prove that if a is a factor of mn, then a is also a factor of hcf(a,m) x hcf(a,n)"

I've been told to use integral linear combination but I don't see how that is relevent??

Any help at all would be much appreciated

Nevermind I've worked it out,

If anyone is interested:

Suppose mn/a. Then there exists an interger q such that mn=qa. Using linear combinations we get hcf(a,m)=ra+sm for some intergers r and s, and hcf(a,n)=ta+bn for some intergers t and b.

Therefore:

Hcf(a,m) x hcf(a,n) = (ra+sm)(ta+bn)
=rt(a^2)+rabn+smta+smnb
=rt(a^2)+rabn+smta+sqab using (mn=qa) from above
=a(rta+rbn+smt+sqb)

So that (hcf(a,m)xhcf(a,n))/a