In the preceding computations, we have found the set of common positive divisors of a = 223092870 and b = 6227020800, and have found the set of positive divisors of gcd(a, b). Compare these two sets. Change the values of a and b, and repeat the experiment: compute the set of common positive divisors of a and b, compute the set of positive divisors of gcd(a, b), and compare the two sets. Once you think you see a pattern, state a conjecture and try to prove it!

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