Consider the number 539. Note that 539 = 72 x 11. (a) How many different values of a can you choose so that 7° is a factor of 539? Explain how you arrived at your answer. (b) How many different values of b can you choose so that 11° is a factor of 539? Explain how you arrived at your answer. (c) As discussed in class, we know that any factor of 539 must be made up of sevens and elevens. In other words, any factor of 539 can be expressed as 7* x 11" for some r and y. Use this fact and your work in the previous two parts to determine how many factors 539 will have without actually finding any of them. Explain how you arrived at your answer.
Consider the number 539. Note that 539 = 72 x 11. (a) How many different values of a can you choose so that 7° is a factor of 539? Explain how you arrived at your answer. (b) How many different values of b can you choose so that 11° is a factor of 539? Explain how you arrived at your answer. (c) As discussed in class, we know that any factor of 539 must be made up of sevens and elevens. In other words, any factor of 539 can be expressed as 7* x 11" for some r and y. Use this fact and your work in the previous two parts to determine how many factors 539 will have without actually finding any of them. Explain how you arrived at your answer.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 92E: DISCUSS: Complementary Combinations Without performing any calculations, explain in words Why the...
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Transcribed Image Text:1. Consider the number 539. Note that 539 = 72 x 11.
(a) How many different values of a can you choose so that 7ª is a factor of 539? Explain
how you arrived at your answer.
(b) How many different values of b can you choose so that 11 is a factor of 539? Explain
how you arrived at your answer.
(c) As discussed in class, we know that any factor of 539 must be made up of sevens and
elevens. In other words, any factor of 539 can be expressed as 7" x 11º for some r and
y. Use this fact and your work in the previous two parts to determine how many factors
539 will have without actually finding any of them. Explain how you arrived at your
answer.
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