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How many prime factors are there in prime factorization of 5005?
A. 2
B. 4
C. 6
D. 7

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Last updated date: 03rd Mar 2024
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IVSAT 2024
Answer
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Hint: We use the concept of prime factorization and write all prime factors of the given number and collect the powers of each prime factor using the law of exponents.
* Any number is said to be a prime number if it has no other factors other than 1 and the number itself.
* Prime factorization is a process of writing a number in multiple of its factors where all factors are prime numbers.
* Law of exponents states that when the base is same we can add the powers of that element i.e. \[{p^m} \times {p^n} = {p^{m + n}}\]

Complete step by step solution:
We have to find the number of prime factors of the number 5005?
We know prime factorization of a number is the representation of a number in terms of multiples of its prime factors.
\[ \Rightarrow 5005 = 5 \times 7 \times 11 \times 13\]
Since no prime factor is repeated in the multiplication in RHS we cannot apply exponent rule as the prime factors are already in simplest form.
Since 5, 7, 11 and 13 are prime numbers and are factors of the number 5005 we can write 5, 7, 11 and 13 are prime factors of 5005.
Number of prime factors of 5005 is 4.

\[\therefore \]Correct option is B.

Note: Many students make the mistake of choosing option D as they might think we have to choose the prime factor of the given number and only option D has one of the prime factors. Carefully choose the option as the question is asking for the number of prime factors so we count the number of factors.
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