Multiple choice

What is the greatest number which divides 392, 486 and 627 so as to leave the same remainder in each case?

  1. 47

  2. 43

  3. 37

  4. 34
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the GCD be d. Then 392 = ad + r, 486 = bd + r, 627 = cd + r. Subtracting: 94 = d(b-a), 235 = d(c-b). GCD of 94 and 235 is 47. Checking: 392 ÷ 47 = 8 remainder 16, 486 ÷ 47 = 10 remainder 16, 627 ÷ 47 = 13 remainder 16. The same remainder is 16, so 47 is correct.

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