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Can 2 numbers have the same prime factorization?
Only if they're the same number. Every composite number has a unique prime factorization.
What are the prime numbers 1-6?
1 can be seen as a unique number or a prime number depending on who you ask. 2, 3, 5 are other prime numbers in this set
What is a Prime Factorization and What is an example?
A prime factorization is the unique way to list any integer greater than 1 as a product of prime numbers. An example of the prime factorization of a composite number is 20=2*2*5 or 20=2^2*5. The prime factorization of a prime number is itself. e.g. 11=11.
Composite number as the product of prime numbers?
It is the unique prime factorisation theorem.
Why is it important that the number one is not a prime number?
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1[note 1] either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.[3][4][5] For example,1200 = 24 × 31 × 52 = 3 × 2 × 2 × 2 × 2 × 5 × 5 = 5 × 2 × 3 × 2 × 5 × 2 × 2 = etc.The theorem is stating two things: first, that 1200 canbe represented as a product of primes, and second, no matter how this is done, there will always be four 2s, one 3, two 5s, and no other primes in the product.The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (e.g. 12 = 2 × 6 = 3 × 4).This theorem is one of the main reasons for which 1 is not considered as a prime number: if 1 were prime, the factorization would not be unique, as, for example, 2 = 2×1 = 2×1×1 = ...
