I understand what is meant by proper factors, e.g. the proper factors of 36 are 2, 3, 4, 6, 9, 12, & 18. However I've just seen the phrase "maximal proper factors" used in the context of determining if a polynomial is primitive.
My best guesses are:
- Maximal proper factors are the greatest two factors of an integer, e.g. for 36 it would be 18 and 12.
- Maximal proper factors are the greatest of each pair of factors of an integer, e.g. for 36 it would be 18, 12, 9, and possibly 6.
Could anyone clarify this? Thanks!
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$\begingroup$I would expect a "maximal proper factor" to mean a factor that doesn't divide any other proper factor.
In other words, I would interpret "maximal" to refer to the divisibility relation.
The maximal proper factors of 36 would then be 18 and 12.
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