3. Consider the numbers A and B below. A = 235 × 512 × 7²1 B = 223 x 37 x 732 (a) Consider the number 2". If possible, find a value of n so that 2" is a factor of A but not of B. If it is not possible, why not? (b) Consider the number 2". If possible, find a value of n so that 2" is a factor of B but not of A. If it is not possible, why not? (c) Consider the number 2". What is the largest value of n you could choose so that 2" is a factor of both A and B. (d) Explain how to use the prime factorization of A and B to find the greatest common factor of A and B. (e) After hearing your explanation, Max asks, "Why do we take the smaller exponent when we are finding the greatest common factor? Shouldn't we take the larger exponent?" Explain to Max why we take the smaller exponent.

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