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) Compute the smallest prime factor of 2197.

) Compute the smallest prime factor of 2197.

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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**Task:** Compute the smallest prime factor of 2197. **Explanation:** To find the smallest prime factor of 2197, we need to test divisibility by prime numbers, starting from the smallest: 2, 3, 5, 7, etc. 1. **Divisibility by 2:** 2197 is an odd number, so it is not divisible by 2. 2. **Divisibility by 3:** The sum of the digits of 2197 (2 + 1 + 9 + 7 = 19) is not divisible by 3. 3. **Divisibility by 5:** 2197 does not end in 0 or 5, so it is not divisible by 5. 4. **Divisibility by 7:** Use the divisibility rule or direct division to check if 2197 is divisible by 7. After calculating, it turns out that 2197 is divisible by 13. So, the smallest prime factor of 2197 is 13.
Transcribed Image Text:**Task:** Compute the smallest prime factor of 2197. **Explanation:** To find the smallest prime factor of 2197, we need to test divisibility by prime numbers, starting from the smallest: 2, 3, 5, 7, etc. 1. **Divisibility by 2:** 2197 is an odd number, so it is not divisible by 2. 2. **Divisibility by 3:** The sum of the digits of 2197 (2 + 1 + 9 + 7 = 19) is not divisible by 3. 3. **Divisibility by 5:** 2197 does not end in 0 or 5, so it is not divisible by 5. 4. **Divisibility by 7:** Use the divisibility rule or direct division to check if 2197 is divisible by 7. After calculating, it turns out that 2197 is divisible by 13. So, the smallest prime factor of 2197 is 13.
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