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Find the number of positive integer divisors of a) 36 b) 99 c) 144 d) 2-3-5-7-11-13-17-19 e) 2-32-5³-74-115-134-175-195 20!. f)

Find the number of positive integer divisors of a) 36 b) 99 c) 144 d) 2-3-5-7-11-13-17-19 e) 2-32-5³-74-115-134-175-195 20!. f)

Advanced Engineering Mathematics
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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**Exercise 2: Finding the Number of Positive Integer Divisors** Determine the number of positive integer divisors for each of the following: a) \(36\) b) \(99\) c) \(144\) d) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19\) e) \(2^3 \cdot 3^2 \cdot 5^3 \cdot 7^4 \cdot 11^5 \cdot 13^4 \cdot 17^5 \cdot 19^5\) f) \(20!\) **Instructions:** Use the formula for finding the number of divisors from the prime factorization of a number. If a number \( n \) can be expressed as \( n = p_1^{a_1} \cdot p_2^{a_2} \cdot \ldots \cdot p_k^{a_k} \), then the number of positive divisors of \( n \) is given by \((a_1+1)(a_2+1)\cdots(a_k+1)\).
Transcribed Image Text:**Exercise 2: Finding the Number of Positive Integer Divisors** Determine the number of positive integer divisors for each of the following: a) \(36\) b) \(99\) c) \(144\) d) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19\) e) \(2^3 \cdot 3^2 \cdot 5^3 \cdot 7^4 \cdot 11^5 \cdot 13^4 \cdot 17^5 \cdot 19^5\) f) \(20!\) **Instructions:** Use the formula for finding the number of divisors from the prime factorization of a number. If a number \( n \) can be expressed as \( n = p_1^{a_1} \cdot p_2^{a_2} \cdot \ldots \cdot p_k^{a_k} \), then the number of positive divisors of \( n \) is given by \((a_1+1)(a_2+1)\cdots(a_k+1)\).
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