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.

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.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

3. Consider the numbers A and B below.
A = 235 × 512 × 721
B = 223 × 37 × 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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