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Unique factorization usually means that any integer can only be factored in one way using prime numbers only:
24 = 2 x 2 x 2 x 3 (unique prime factorization)
If other numbers than prime numbers are allowed, factorization is not unique.
24 = 2 x 12 = 3 x 8 = 4 x 6 = -4 x -6 = etc. (non-unique factorization)
If 1 is allowed, then every number has an infinity of factorizations:
5 = 1 x 5 = 1 x 1 x 5 = 1 x 1 x 1 x 5 = etc.
So, limiting the allowed factors to prime numbers, makes the factorization unique.
The theorem is that every integer has a unique prime factorization. So, the answer to your question could be any number showing its unique prime factorization.
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Does each natural number greater than one have its own unique prime factorization?
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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.
How many prime factorization of the number 120 can there be?
Every number's prime factorization is distinct. 2 x 2 x 2 x 3 x 3 x 5 = 120
What is the largest prime factor of a composite number?
Each composite number has its own unique prime factorization. The largest number in that factorization would be the largest prime factor. It will never be more than half of the original number.
What is unique factor?
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 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.
Can you give me brief notes on factorization and examples?
All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this. Example: 210 210 Divide by two. 105,2 Divide by three. 35,3,2 Divide by five. 7,5,3,2 Stop. All the factors are prime. 2 x 3 x 5 x 7 = 210 That's the prime factorization of 210.
