The number must divide (2272 - R) and (875 - R) for some remainder R. This implies the number must divide the difference (2272 - 875) = 1397. Factoring 1397 gives 11 * 127. Thus, 127 is the divisor.
The required number must perfectly divide the difference between the two values. First, subtract the smaller number from the larger number to get 2272 - 875 = 1397. We then test the options to see which one divides 1397 without a remainder; 127 multiplied by 11 is exactly 1397. The result is 127.