The term common factoring is relating to what is common among two or more things. This same technique is used in math. In math some problems require the common factor to be found. A common factor of the numbers 4 and 8 would be the number 2.
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1. Factoring out a common monomial 2. Factoring out the differnece of two perfect square numbers 3. Factoring out a common binomial
Reducing fractions to their lowest terms by finding their highest common factor of the numerator and denominator When adding or subtracting fractions with different denominators by finding their lowest common multiple
When you divide 2 or more numbers by a common factor which is not the greatest common factor, they will still have a common factor which is greater than 1. When you divide them by their greatest common factor, the quotients are coprime - that is, they no longer have a factor in common other than 1.
Yes, if they are in common for all the terms.
What makes a greatest common factor "common" is comparing at least two terms and finding something common between them.