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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22b9d752-056b-4334-94b2-a971ee1a8115%2F9e2d0387-330d-4103-90cf-edf74a40efb2%2Fzou92k.jpeg&w=3840&q=75)
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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