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1. Find the sum of the positive integer divisors of a) 35 e) 2-3-5-7-11 b) 196 f) 25345³7²11 c) 1000 d) 2100 g) 10! h) 20!.

1. Find the sum of the positive integer divisors of a) 35 e) 2-3-5-7-11 b) 196 f) 25345³7²11 c) 1000 d) 2100 g) 10! h) 20!.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Exercise 1: Finding the Sum of Positive Integer Divisors** For each of the following numbers, calculate the sum of all positive integer divisors: a) 35 b) 196 c) 1000 d) \(2^{100}\) e) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\) f) \(2^3 \cdot 4^5 \cdot 3^7 \cdot 11\) g) \(10!\) h) \(20!\) **Explanation:** The goal is to determine the sum of divisors for each specified number. In mathematical terms, the sum of the divisors function, denoted as \(\sigma(n)\), gives us the sum of all positive divisors of \(n\). For each option, apply the formula or method applicable for that structure (e.g., prime factorization may be helpful). You'll need to understand and use concepts like prime factorization, factorials, and divisor functions to compute the answers.
Transcribed Image Text:**Exercise 1: Finding the Sum of Positive Integer Divisors** For each of the following numbers, calculate the sum of all positive integer divisors: a) 35 b) 196 c) 1000 d) \(2^{100}\) e) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\) f) \(2^3 \cdot 4^5 \cdot 3^7 \cdot 11\) g) \(10!\) h) \(20!\) **Explanation:** The goal is to determine the sum of divisors for each specified number. In mathematical terms, the sum of the divisors function, denoted as \(\sigma(n)\), gives us the sum of all positive divisors of \(n\). For each option, apply the formula or method applicable for that structure (e.g., prime factorization may be helpful). You'll need to understand and use concepts like prime factorization, factorials, and divisor functions to compute the answers.
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