3. In the following, a factor may be prime, composite or 1. Note that 6 has 4 factors (1, 2, 3 and 6) and 16 has 5 factors (1, 2, 4, 8 and 16). a. What is the smallest positive integer with exactly 15 factors? b. What is the smallest positive integer with exactly 16 factors? c. For a given positive integer n, describe a method for finding the smallest positive integer with exactly n factors.

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3. In the following, a factor may be prime, composite or 1. Note that 6 has 4 factors (1, 2,
3 and 6) and 16 has 5 factors (1, 2, 4, 8 and 16).
a. What is the smallest positive integer with exactly 15 factors?
b. What is the smallest positive integer with exactly 16 factors?
c. For a given positive integer n, describe a method for finding the smallest
positive integer with exactly n factors.
Transcribed Image Text:3. In the following, a factor may be prime, composite or 1. Note that 6 has 4 factors (1, 2, 3 and 6) and 16 has 5 factors (1, 2, 4, 8 and 16). a. What is the smallest positive integer with exactly 15 factors? b. What is the smallest positive integer with exactly 16 factors? c. For a given positive integer n, describe a method for finding the smallest positive integer with exactly n factors.
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