Question

Consider the statements regarding prime factorization:

Statement I: The factors in prime factorization of a number are prime numbers.

Statement II: The numbers, having composite numbers as factors, cannot be expressed as prime factorization.

• A. Both the statements are correct.
• B. Only Statement I is correct.
• C. Only Statement II is correct.
• D. None of the above.

Answer 1

The correct option is B Only Statement I is correct.

Expressing the factors of a number as prime numbers is called prime factorization.
For example: $24=1\times 8\times 3$
$\Rightarrow 24=1\times 2\times 2\times 2\times 3$
Here, all the factors are prime numbers.
$\therefore$ Statement I is correct.

Also, $8$, a composite number, is a factor of $24.$
However, $8$ can be expressed as $2\times 2\times 2,$ where $2$ is a prime number.
$\therefore$ Statement II is not correct.