What is the largest four-digit integer whose HCF equals 144___________?
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Answer: D. 9936
Explanation
The largest four-digit integer is nine thousand nine hundred ninety-nine, which serves as the upper boundary for our calculation. Dividing nine thousand nine hundred ninety-nine by the given HCF of one hundred forty-four gives sixty-nine point forty-three. Multiplying the whole number sixty-nine by one hundred forty-four yields the largest valid four-digit multiple as nine thousand nine hundred thirty-six. The highest common factor, or HCF, divides evenly into all multiples of that number. Finding the largest four-digit multiple requires dividing the maximum four-digit number by the HCF and multiplying the floor integer result. Any multiple exceeding sixty-nine times the HCF will result in a five-digit number exceeding nine thousand nine hundred ninety-nine.
Option A is not a proper multiple of the one hundred forty-four HCF value. Option B results in a non-integer quotient when divided by the required HCF factor. Option C is not divisible evenly by one hundred forty-four, violating the fundamental HCF property.
- Subject
- Mathematics
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- Mathematics
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