Dividing the integers 4242 and 2903 by a specific three-digit number yields an identical remainder in both instances. Identify this number?
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Answer: B. 103
Explanation
Dividing both forty two forty two and twenty nine zero three by a common divisor leaves identical remainders. Calculating the difference between the two numbers removes the unknown remainder from the equation. Finding the greatest common divisor of the resulting difference identifies the three digit number as one hundred three. Numbers that leave the same remainder when dividing a target integer share a common divisor relationship. Subtracting two numbers that yield identical remainders eliminates the remainder term completely. The divisor must be a factor of the absolute difference between the two original numbers.
Number theory algorithms use greatest common divisor properties to simplify modular arithmetic problems. Cryptography protocols rely on remainder properties and common divisors for encryption key generation. Arithmetic problem solving often uses difference properties to isolate unknown divisor values. Option a fails to divide both numbers with an identical remainder outcome. Option c produces different remainders when tested against the two original integers. Option d does not satisfy the divisibility condition for leaving an equal remainder.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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