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According to the Fundamental Theorem of Arithmetic, if p (a prime number) divides b2 and b is positive, then ________.
  • a)
    b divides p
  • b)
    b2 divides p
  • c)
    p divides b
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
According to the Fundamental Theorem of Arithmetic, if p (a prime numb...
Explanation:
The Fundamental Theorem of Arithmetic states that every positive integer greater than 1 can be uniquely represented as a product of primes.
Let's say that p divides b2 and p is a prime number. This means that p must be one of the prime factors of b2.
We can write b2 as a product of primes: b2 = p1a1 * p2a2 * … * pnan, where p1, p2, …, pn are prime numbers and a1, a2, …, an are positive integers.
Since p divides b2, p must be one of the prime factors in the prime factorization of b2. Let's say that p occurs with a power of k in the prime factorization of b2.
So, we can write b2 = pk * (p1a1-k * p2a2 * … * pnan).
Since b is positive, b2 is positive and so pk is positive. Therefore, p divides b.
Hence, the correct answer is option 'C', p divides b.
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Community Answer
According to the Fundamental Theorem of Arithmetic, if p (a prime numb...
If p divides b2, then p also divides b.
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According to the Fundamental Theorem of Arithmetic, if p (a prime number) divides b2 and b is positive, then ________.a)b divides pb)b2 divides pc)p divides bd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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