No zero is not a factor. Its very attributes prevent it from being a factor of any non-zero number and since 0 times any number is equal to zero, it does not tell us the relationship between the number and zero that creates the number being factored (i.e. 12 = 6*2, therefore, those factors show their relative effect in creating 12.)
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Yes. Every integer is a factor of zero. Zero is in fact the only number that can be divided by zero, so zero is also a factor. Zero has an infinite number of factors.
No.
Zero is only a factor of zero. If I have 0 and multiply it by any other number, I still get 0. No number can be divided by zero - the concept is meaningless.
Zero is not a factor of 4. Zero is only a factor of zero! The factors of 4 are 1, 4, 2 The factors of zero are zero and any other number. Therefore the common factors are 1,2 and 4
Any non-zero integer can be a common factor.