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Q: When any composite number is written as the product of all its prime numbers?

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No they cannot. the factors of prime numbers are 1 and itself. if its factor has a composite number, then the original number would be composite.

the prime factorization of the number

Yes, by definition!

the prime factorization

Prime factorization is writing a composite number as a product of prime numbers.

composite

A composite number.

Yes. For example 6 can be written as 2 x 3.

Composite numbers can be written that way.

A composite number is the product of two or more prime numbers.

Yes, of course. In fact the product of any two numbers is composite unless one of them is 1.

Showing a composite number as a product of prime numbers is called prime factorization.

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