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## Main Question or Discussion Point

Do they use the Euclidean Algorithm?

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- Thread starter matqkks
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Do they use the Euclidean Algorithm?

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mathman

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jedishrfu

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jedishrfu

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https://en.m.wikipedia.org/wiki/Euclidean_algorithm

I imagine math software would use this algorithm to compute it as subtractions are relatively cheap compared to multiplications or divisions.

Another remote possibility is it uses a combination of lookup table and Euclidean algorithm to speed things up although that may take up more memory than necessary and depending on the table size more costly time wise.

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mfb

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You still need some sort of division to calculate how much you have to subtract. Simply subtracting the smaller number from the larger number repeatedly has a really bad worst-case runtime if the numbers are very different (exponential, while divisions make the method scale with the input length squared).I imagine math software would use this algorithm to compute it as subtractions are relatively cheap compared to multiplications or divisions.

There are alternative algorithms that can compute the GCD faster than quadratic runtime for longer inputs.

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