We break down the classic Project Euler Problem 3—finding the largest prime factor of a colossal number—starting with the small example 13195 (factors 5, 7, 13, 29). Then we explore an efficient Python approach: test small primes, divide to shrink the problem, and keep a list of found factors. We also discuss extending the method to find all prime factors and ponder scaling to cryptography-sized numbers.

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