6 and any multiple greater than 1 of 6, eg 6 and 12, 6 and 18, 6 and 24, etc...
Any two multiples of 6 where the other factors are relatively prime (ie have a gcf of 1), eg 6 and 7 are relatively prime, so 6 x 6 = 36 and 6 x 7 = 42 have a gcf of 6, 2 and 9 are relatively prime, so 2 x 6 and 9 x 6 (12 and 54) have a gcf of 6, etc.
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The factors of 6 are 1, 2, 3 and 6. For them to be common, they need to be compared to another set of factors.
No single number has a "common" factor.
"Common" means "same for both". A 'common' factor is a number that's a factor of 2 or more numbers.
2 and 3
Always equal to or less than the smaller number, yes.
When they have a factor in common greater than one.
Lots of numbers are NOT common factors. For example, 5, 7, 100...Get the greatest common factor of both numbers. All common factors are factors of this greatest common factor. Note that all of them must needs be less than or equal to the greatest common factor. Any other number is NOT a common factor.
The product of the GCF and LCM is equal to the product of the original two numbers.