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Q: Why does every number have a prime factorization?

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Every number's prime factorization is distinct. 2 x 2 x 2 x 3 x 3 x 5 = 120

53 is a prime number so there is no relevant prime factorization for it.

12 is not a prime factorization.

factorization

That's the prime factorization of 18.

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Yes

No. Prime numbers are already prime. Every composite number has a prime factorization.

Every composite number has its own unique prime factorization.

Every composite number has its own unique prime factorization.

Every prime number has exactly 2 factors, 1 and the number itself.

Only if they're the same number. Every composite number has a unique prime factorization.

Every positive composite number only has one unique prime factorization.

Every number's prime factorization is distinct. 2 x 2 x 2 x 3 x 3 x 5 = 120

No. Every composite number has one unique prime factorization. You can write it with or without exponents, but it's still the same prime factorization.

the prime factorization

The prime number is the prime factorization. For example, the prime factorization of the prime number 3 is 3. Get it?

No, just composite numbers.

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