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The way I do it: first look at the number to see if there are any factors that can be recognized, such as 2, 3, 5, 9, 10. There are ways to recognize if a number is divisible by these numbers.

If the number is divisible by any of those, then perform that division, and then check again (example there is no easy check for divisible by 27, but if you divide the number by 9, then the quotient will be divisible by 3). Keep track of what you're dividing by. Next you will just have to start testing dividing the number by primes: 7, 11, 13, 17, etc.

Then, if you determined that you divided a number by 10, for example, the prime factors for 10 are 2 and 5. Do the same for 9 is prime factors of 3 and 3.

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Q: What are the methods of prime factorization?
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