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Let N = 34 · 34 · 63 - 270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N ? (A) 1 : 16 (B) 1 : 15 (C) 1 : 14 (D) 1 : 8 (E) 1 : 3

Let N = 34 · 34 · 63 - 270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N ? (A) 1 : 16 (B) 1 : 15 (C) 1 : 14 (D) 1 : 8 (E) 1 : 3

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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Let N = 34 · 34 · 63 · 270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N ? (A) 1 : 16 (B) 1 : 15 (C) 1 : 14 (D) 1 : 8 (E) 1 : 3
Transcribed Image Text:Let N = 34 · 34 · 63 · 270. What is the ratio of the sum of the odd divisors of N to the sum of the even divisors of N ? (A) 1 : 16 (B) 1 : 15 (C) 1 : 14 (D) 1 : 8 (E) 1 : 3
Expert Solution
Step 1

We have the number N given by N=34·34·63·270. From the basics learned in the earlier stages, we have

34=2·1734=2·1763=3·3·7270=2·3·3·3·5

We now have 

N=2·17·2·17·3·3·7·2·3·3·3·5N=23·35·5·7·172

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