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What's a good approach for identifying potentially large common factors?

For example, how do I quickly recognise that 123543/99900 is reducible to 371/300?

Or putting this another way, how do I efficiently work out that 123543 and 99900 have the common factor 333?

fractor
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    Do you know about the Euclidean algorithm? Check it out in wikipedia. See https://math.stackexchange.com/questions/3379695/why-does-the-euclidean-algorithm-for-finding-gcd-work/3379763#3379763 – Ethan Bolker May 10 '21 at 22:01
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    Short answer: learn small divisibility rules. – Sean Roberson May 10 '21 at 22:05
  • Test each number as a factor which is smaller than its square root. Also, context and your attempts at the problem are well. You may read this, even though you received the cross account reputation bonus. – Тyma Gaidash May 10 '21 at 22:12
  • @SeanRoberson That won't help much with big numbers. And the OP wants the greatest common factor, not all the factors. – Ethan Bolker May 10 '21 at 23:58
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    @TymaGaidash That won't help much with big numbers. And the OP wants the greatest common factor, not all the factors. – Ethan Bolker May 10 '21 at 23:59

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