Two numbers have a product of 2160 and an HCF of 12. Find the numbers________?
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Answer: A. (36,60)
Explanation
Let the numbers be represented as twelve x and twelve y based on the given highest common factor of twelve. The product of the numbers is one forty four times x times y, which equals twenty one sixty, making x times y equal to fifteen. The coprime factor pairs of fifteen are one and fifteen or three and five, yielding the number pair thirty six and sixty. Any two numbers with a known highest common factor can be expressed as multiples of that factor. Coprime numbers share no common positive integer factors other than one. The product of two numbers divided by the square of their highest common factor equals the product of their coprime factors.
Option B is incorrect because the product of twelve and one eighty does not equal twenty one sixty. Option C features numbers whose product and highest common factor do not match the given parameters. Option D fails the highest common factor and product verification checks for the problem.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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