State true or false: Every composite number can be factorized as a product of primes, and this factorization is unique.

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True

False

answer is A.

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Detailed Solution

Given is the statement that every composite number can be factorized as a product of primes, and this factorization is unique.
All the numbers which have factors other than 1 and the number itself are termed as composite numbers.
Also, the factors of all the composite numbers are unique and so is their factorization.
For example:

9 = 3 × 3

, has three factors viz., 1, 3 and 9 and all are unique.

21 = 3 × 7

, has 4 factors viz., 1, 3, 7 and 21 and all are unique.
Also, in the above examples, we can observe that the numbers in the product of factors, i.e., 3 and 7 are prime.
Similarly, there can be many more examples and for all the composite numbers, the factors and factorizations will be unique.
Hence, the statement is true.
So, the correct option is 1.

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