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An unnecessary one. 42 + 96 = 138
The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. YOu have only one term "8 + W" in the question so there cannot be a GCF. It is not possible to find any factor (other than 1 and 8 + W, itself, without further information about W.The distributive property has no relevance to this question.
The GCF is 6.
9 + 36 = (9 x 1) + (9 x 4) = 9 x 5 = 45
It allows you to find all the factors of a number. Prime factorisation is necessary for calculating the greatest common factor and least common multiple of sets of numbers. That information is essential for working with rational numbers.