What is the smallest five-digit integer sharing an HCF of 144__________?
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Answer: B. 10080
Explanation
The smallest five-digit integer begins at ten thousand as the baseline numerical threshold. Dividing ten thousand by the highest common factor one hundred forty six gives sixty nine point four. Multiplying the next whole integer seventy by one hundred forty four yields the exact value ten thousand eighty. The highest common factor represents the largest integer that divides evenly into both numbers. Multiples of a given HCF are generated by multiplying that factor by successive whole integers. Finding the smallest five-digit multiple requires testing integers around the ten thousand threshold.
Number theory applications require finding specific numerical multiples that satisfy digit length constraints. Industrial batch sizing often requires quantities that are exact multiples of standard machine capacities. Understanding HCF multiples helps solve complex divisibility puzzles in competitive examinations. Option A suggests ten thousand eighty five which is not an exact multiple of the given HCF. Option C suggests ten thousand seventy five which falls below the five-digit threshold requirement. Option D suggests ten thousand seventy which fails the exact divisibility check for one forty four.
- Subject
- Mathematics
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- Mathematics
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- —
- Difficulty
- medium
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