Multiple choice

Find the greatest number that will divide 385, 435 and 541 leaving remainders 11, 10 and 14, respectively.

  1. 19

  2. 17

  3. 13

  4. 12

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number must divide (385-11)=374, (435-10)=425, and (541-14)=527. GCD(374, 425, 527). 374 = 17*22, 425 = 17*25, 527 = 17*31. The GCD is 17.

AI explanation

We subtract the respective remainders from the given numbers to get 385 minus 11 equals 374, 435 minus 10 equals 425, and 541 minus 14 equals 527. The required number is the HCF of 374, 425, and 527. The difference between 425 and 374 is 51, and the difference between 527 and 425 is 102, so the HCF must be a factor of 51. Testing 17, we find that 374 equals 17 times 22, 425 equals 17 times 25, and 527 equals 17 times 31, confirming the answer is 17.

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