Multiple choice

The greatest number which will divide 116, 221, 356 leaving the same remainder in each case is

  1. 15

  2. 5

  3. 10

  4. 20

  5. 25
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A Correct answer
Explanation

The greatest number dividing a, b, c leaving the same remainder is gcd(|a-b|, |b-c|, |c-a|). |221-116| = 105. |356-221| = 135. |356-116| = 240. gcd(105, 135, 240) = 15.

AI explanation

To find the greatest number that leaves the same remainder when dividing 116, 221 and 356, apply the greatest common divisor (GCD) method to the differences between the numbers. Calculate the differences 221 minus 116 equals 105, and 356 minus 221 equals 135. The required number is the HCF of 105 and 135; since the highest common factor is 15, the required number is 15.

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