Multiple choice

Find the greatest number that will divide 640, 710 and 1526 so as to leave 11, 7 and 9 as remainders respectively

  1. 36

  2. 29

  3. 42

  4. 37
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D Correct answer
Explanation

Find GCD of (640-11), (710-7), (1526-9) = GCD(629, 703, 1517). 629 = 17 * 37. 703 = 19 * 37. 1517 = 41 * 37. The GCD is 37.

AI explanation

To find the required number, subtract the respective remainders from each number to get 629, 703, and 1517. The greatest number that exactly divides these differences is their highest common factor. Using the Euclidean algorithm, the HCF of 629 and 703 is found to be 37, and 37 also perfectly divides 1517. The result is 37.

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