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I find the easiest way to find the prime factorization of any number is to start with the smallest Prime number that divides the number. So, for 50, I would start with 2. Now we have 2x25. Since 25 is 52 we find the prime factorization of 50 is 2x5x5.
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409 is a prime number.
Is there a number with two prime factorizations?
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