Consider the following statements: 1. The HCF of (p + q) and (p2 – q2) is (p + q). 2. The HCF of (p – q) and (p2 – q2) is (p + q). 3. The HCF of (p + q) and (p3 + q3) is (p + q). 4. The HCF of (p – q) and (p3 – q3)  is (p + q). Which of the above statements is/are correct?

Consider the following statements: 1. The HCF of (p + q) and (p2 – q2) is (p + q). 2. The HCF of (p – q) and (p2 – q2) is (p + q). 3. The HCF of (p + q) and (p3 + q3) is (p + q). 4. The HCF of (p – q) and (p3 – q3)  is (p + q). Which of the above statements is/are correct? Correct Answer 1 and 3 only

Concept:

The HCF of two or more numbers is the greatest factor that divides each of them exactly.

Calculation:

Statement 1

The factor of (p + q) = (p + q)

The factor of (p² – q²) = (p + q) (p – q)

The HCF of (p + q) and (p² – q²)

⇒ (p + q)

Statement 2

The factor of (p – q) = (p – q)

The factor of (p² – q²) = (p + q) (p – q)

The HCF of (p – q) and (p² – q²)

⇒ (p – q)

Statement 3

The factor of (p + q) = (p + q)

The factor of (p³ + q³) = (p + q) (p² – p × q + q²)

The HCF of (p + q) and (p³ + q³)

⇒ (p + q)

Statement 4

The factor of (p – q) = (p – q)

The factor of (p³ – q³) = (p – q) (p² + p × q + q²)

The HCF of (p – q) and (p³ – q³)  

⇒ (p – q)

∴ Only statement 1 and 3 are correct.