What is the largest four-digit number whose highest common factor (HCF) with 144 is exactly 144?

Explanation

To find the greatest four-digit number having 144 as its HCF with 144, we need the largest multiple of 144 below 10,000. Dividing 9999 by 144 gives approximately 69.4, so multiplying 144 by 69 yields 9936, which is the highest multiple of 144 under 10,000. Hence, 9936 is the answer.