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Consider the following statements: 1) If p is relatively prime to each of q and r, then p is relatively prime to the product qr. 2) If p divides the product qr and if p divides q, then p must divide r. Which of the above statements is/are correct?

Consider the following statements: 1) If p is relatively prime to each of q and r, then p is relatively prime to the product qr. 2) If p divides the product qr and if p divides q, then p must divide r. Which of the above statements is/are correct? Correct Answer 1 only

Statement 1: If p is relatively prime to each of q and r, then p is relatively prime to the product qr.

Suppose p = 8, q = 15 and r = 7

Here, p is relatively prime to each of q and r.

Now, product qr = 105

Here, p i.e. 8 is relatively prime to qr i.e. 105 also.

Hence, statement 1 is correct.

Statement 2: If p divides the product qr and if p divides q, then p must divide r.

Suppose p = 4, q = 8 and r = 7

Here, qr = 56

Here, p divides the product qr and p divides q also.

But p does not divide r here.

Hence, statement 2 is not correct.

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