Answer
See the explanation
Work Step by Step
We want all factors of $211 397$. If it has any non-trivial factor, one of them must be a prime $p ≤ \sqrt{211 397}\approx460$. We test divisibility by the primes up to $460$:
• $2, 3, 5, 7, 11, 13, …, 457$ → none divide 211 397 evenly.
Do the factors of $211,397$ are $1$ and $211,397$, so the given number is prime.
This problem relates to this chapter by demonstrating how to find the factors of a given number, which is a fundamental concept in number theory. Understanding factors helps in various mathematical operations and problem-solving techniques.
This example illustrates why RSA works: as numbers get larger, factoring (which is easy to state but hard to do) becomes computationally expensive, providing encryption security.
