Every number has at least one factor, the number 1.
Every number greater than 1 has at least two factors, 1 and itself.
Any number with exactly 2 factors is prime.
Any number with more than 2 factors is composite; in this case it can be factorised completely into primes.
The number 1 has only one factor. It is therefore neither prime nor composite.
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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.
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.