Prime Factorization of 25252525 | 2025.12.25

This is a video of the year 2025, and this year's Christmas contains a special moment of 2025.12.25 12:25:25, where the number 25 is repeated 4 times. To commemorate this, let us find the prime factorization of an 8-digit integer 25252525. I will try to solve this problem relying on brute force (dividing by every prime number) as little as possible, and instead try to utilize more interesting properties such as divisibility rule, modular arithmetic, and one very famous theorem related to that. Oh, and of course, HAPPY HOLIDAY!

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