Question

If p and q are two positive integers such that p= a³ b² and q = ab³, where a and b are prime numbers, then HCF (p, q) is

• A. ab
• B. ab²
• C. a³b³
• D. a²b²

Answer 1

The Correct Option is B

Given that \( p = a^3 b^2 \) and \( q = a b^3 \), where \( a \) and \( b \) are prime numbers, we need to find the HCF of \( p \) and \( q \). The prime factorization of \( p \) is: \[ p = a^3 \cdot b^2 \] The prime factorization of \( q \) is: \[ q = a \cdot b^3 \] To find the HCF, we take the lowest powers of the common prime factors. The common prime factors are \( a \) and \( b \). For \( a \), the lowest power is \( a^1 \), and for \( b \), the lowest power is \( b^2 \). Thus, the HCF of \( p \) and \( q \) is: \[ \text{HCF}(p, q) = a \cdot b^2 \]

The correct option is (B): \(ab^2\)