Multiple choice

When 2270, 3739 and 6677 are divided by a certain number of three digit, the remainders are the same. Find the number. संख्यायें 2270, 3739 और 6677 में से प्रत्येक को तीन अंकों की किसी संख्या से भाग देने पर शेषफल समान आता है। संख्या बताइये।

  1. 189

  2. 113

  3. 115

  4. 137
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B Correct answer
Explanation

If remainders are equal, the divisor divides differences: 6677-3739=2938, 3739-2270=1469, 6677-2270=4407. GCD(2938,1469,4407)=1469. So divisor is a 3-digit factor of 1469. 1469=17×7×13. Checking options: only 113 gives remainder 6 with all three numbers.

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