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Can a composite number have more than one prime factorization?
No, a composite number can't have more than one prime factorization.
Why isn't it possible for a composite number to have more than one prime factorization?
Prime factorizations are unique. If you change the prime factorization, you change the number.
What is the prime factorization of 1 and 125?
One doesn't have a prime factorization. The prime factorization of 125 is 5 x 5 x 5.
What is the gfc of 45 and 75?
GCF stands for Greatest Common Factor. This means that the GCF of 45 and 75 will be the greatest common factor of 45 and 75. The prime factorization of 45 is 3^2*5. Thus, a number is a factor of 45 if and only if it does not have more than 2 3s in its prime factorization, more than one 5 in its prime factorization, or any other prime factor. The prime factorization of 75 is 3*5^2. Thus, a number is a factor of 75 if and only if it does not have more than one 3 in its prime factorization, more than 2 5s in its prime factorization, or any other prime factor. Combining those two conclusions together, we get that if a number is a common factor of 45 and 75 if and only if it does not have more than one 3 in its prime factorization, more than one 5 in its prime factorization, or any other prime factor. Since multiplying by a 3 or a 5 will only increase the value of a number, there is no reason to not include them. Thus, the GCF of 45 and 75 is 3*5 or 15.
Is it possible for a composite number to have more than one prime factorization?
No.No.
