Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime: 1. Both p and q may be prime numbers. 2. Both p and q may be composite numbers. 3. One of p and q may be prime and the other composite. Which of the above statements are correct?

Option 4 : 1, 2 and 3

p & q are relatively prime

Relative prime = Two integers are relatively prime if there is no integer greater than one that divides them both

1) so, two prime numbers don’t have common factors so pair of any two of any two prime numbers are always relatively prime

2) Let’s p = 4 & q = 9 which are composite numbers

Factor of p = 4 = 2 × 2 × 1

Factors of q = 9 = 3 × 3 × 1

They don’t have any common factors

So, they are relatively prime

3) Let’s say p = 3 & q = 8

Factors of P = 3 × 1

q = 8 = 2 × 2 × 2 × 1

So, they don’t have any common factors, so they are relatively prime