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.

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