Multiple choice

When 2270, 3739 and 6677 are divided by a certain three-digit number, the remainders are the same. Find the number.

  1. 111

  2. 112

  3. 113

  4. 132

  5. 134
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 2270, 3739, and 6677 all give same remainder r when divided by d, then: (3739-2270) = 1469, (6677-3739) = 2938, (6677-2270) = 4407. All differences must be divisible by d. Finding GCD: 2938 = 2 × 1469, 4407 = 3 × 1469. So d must divide 1469. 1469 = 13 × 113. Checking options: 113 is a three-digit divisor and 1469 is divisible by it.

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