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This answer is in the context of numbers that are likely to crop up in school or graduate mathematics, not in cryptology or advanced research.

Complete factorisation of large numbers is tedious and may require a lot of false starts (if the next factor is quite large). So, for large numbers I would start with Euclid's algorithm (see link). All that is required for this process is subtraction. The problem of finding the GCF of two large numbers soon becomes that of finding the GCF of two very much smaller numbers. Although the method can be carried out to the end, I will often choose to switch to factorisation when the numbers are smaller: below 400, say, when all you need to know is the times tables to 20. Given all the divisibility rules, this is not as daunting as it may sound.

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10y ago
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Wiki User

8y ago

Prime factorization: fast and easy.

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Q: What method do you like best for gcf why?
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