What is the greatest number that leaves remainders of 6 and 5 when dividing 1657 and 2037 respectively_________?
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Answer: B. 127
Explanation
Subtracting the respective remainders from each number gives sixteen fifty one and twenty thirty two. The greatest number required must be the highest common factor of these two adjusted values. Calculating the highest common factor of sixteen fifty one and twenty thirty two yields one twenty seven. The highest common factor represents the largest positive integer that divides evenly into a set of numbers. Subtracting specified remainders converts a division problem into a standard common factor task. Euclidean algorithm methods provide an efficient way to find greatest common divisors for large integers.
Modular arithmetic applications use remainder properties to solve distribution and scheduling problems. Computer science algorithms rely on greatest common divisor calculations for data encryption. Industrial partitioning tasks often require finding maximum common divisor lengths for raw materials. Option A is incorrect because it does not divide both adjusted numbers without leaving a remainder. Option C overestimates the common divisor and fails the division tests for the adjusted values. Option D is a large distractor value that does not divide the adjusted numbers evenly.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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