Let the highest common factor (HCF) of two positive integers a and b be 12, with a > b > 12. Which ordered pair (a, b) satisfies these conditions?

Introduction / Context:This item checks understanding of the definition of HCF and the implications for the possible forms of a and b. If HCF(a, b) = 12, both a and b must be multiples of 12, and no larger common factor may divide both simultaneously.

Given Data / Assumptions:

• a and b are positive integers.
• HCF(a, b) = 12.
• a > b > 12.

Concept / Approach:Write a = 12x and b = 12y with HCF(x, y) = 1. The inequality a > b > 12 implies x > y ≥ 2 (since b > 12 must be at least 24). Check each option against these conditions and verify the HCF directly if needed.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• (12, 24) and (24, 12) do not satisfy a > b > 12 as required.
• (24, 36) does not have a > b; it is reversed and also b = 36 is not less than a.

Common Pitfalls:

• Forgetting that HCF imposes co-primeness on the scaled-down pair (x, y) and missing the strict order a > b > 12.

Final Answer: