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Suppose two natural numbers a, b satisfy ab = n for some fixed integer n. What is the maximum possible value of gcd(a, b)?

Let $d= gcd (a,b)$
So, $d= xa + yb$
I don't know how to proceed with this. Is the answer n?

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If $d$ divides both $a$ and $b$, then $d^2$ divides $n$.

So the largest possible value for $d$ is the square root of the largest square factor of $n$.

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