Two numbers have a product of 4107 and an H.C.F of 37. What is the larger number_________?
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Answer: C. 111
Explanation
Expressing the numbers as multiples of their highest common factor establishes a clear algebraic product relationship. Dividing the total product by the square of the HCF yields the product of the two remaining coprime factors. Multiplying the HCF by the larger coprime factor three gives the exact value of one hundred eleven. The highest common factor divides evenly into all numbers sharing that greatest common divisor relationship. Any two integers can be expressed as their HCF multiplied by two distinct coprime integer factors. The product of two numbers equals the product of their HCF and their least common multiple.
Option A suggests one hundred one which is not a multiple of the thirty-seven highest common factor. Option B suggests one hundred seven which is not divisible by thirty-seven without leaving a remainder. Option D suggests one hundred eighty-five which corresponds to a different factor pair multiplication result.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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