SOLUTION: Hello, Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?

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Question 904939: Hello,
Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?
Found 2 solutions by richwmiller, rothauserc:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a) the prime factors might be written in a different style or order but they will have the same numbers listed
b) prime numbers have no further factorization

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We consider whole numbers greater than 1 and NOT fractions:
1) It is a Composite Number when it can be divided evenly
by numbers other than 1 or itself.
2) It is a Prime Number when it can't be divided evenly by any number
(except 1 or itself).
a) Now we can consider "The Fundamental Theorem of Arithmetic", this Theorem states; "that every integer greater than 1 either is prime itself or is the product of prime numbers, and that, although the order of the primes in the second case is arbitrary, the primes themselves are not"
Therefore there is only one prime factorization of a composite number.
You can find the proof on the Internet.
b) 1 has no prime factors