Question

A composite number can be written as a product of prime numbers in

• A. a unique way
• B. at least two ways
• C. any number of ways
• D. None

Answer 1

The Correct Option is A

A composite number is a number that can be factored into two or more prime numbers. However, this factorization is always unique, as per the Fundamental Theorem of Arithmetic, which states that every composite number can be written as a product of prime numbers in a unique way, except for the order of the prime factors. For example:
\( 12 = 2 \times 2 \times 3 \)
\( 144 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \)
In each case, the product of prime factors is unique (though the order of multiplication can vary). Thus, a composite number can always be written as a product of prime numbers in a unique way. 

The correct answer is option (A): a unique way