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No, that's just a factor. A common factor is when that factor is also a factor of another number.
The greatest factor of a number is the number itself.
A factor is a number that divides evenly into another number with no remainder. 3 is a factor of 9. 4 is not a factor of 9.
The greatest factor of any number is the number itself. There is no integer that is the greatest factor of every number. One is a factor of every number. One is the GCF of co-prime numbers.
A factor is a number or quantity that when multipled with another produces a given number or expression.