Multiple choice

Find the greatest number that will divide $445,\,572\;and\;699$ leaving remainders $4,\,5\,\,6$ respectively.

  1. $64$
  2. $63$
  3. $44$
  4. $21$
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B Correct answer
Explanation

To find the greatest number, subtract the remainders from the numbers: 445-4=441, 572-5=567, and 699-6=693. The greatest common divisor of 441, 567, and 693 is 63.

AI explanation

To find the greatest number, we first subtract the respective remainders from the given numbers to get 441, 567 and 693. The required number is the highest common factor of these three differences. Using the Euclidean algorithm or prime factorization, the HCF of 441, 567 and 693 is found to be 63. Therefore, the greatest number that satisfies the condition is 63.

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